The source files for all examples can be found in /examples.
Portfolio Optimisation
We consider a single-period Markowitz portfolio optimisation example. Assume that we have a portfolio with $n$ assets at the beginning of time period $t$. Given some forecasts on risks and expected returns we try to find the optimal trade vector that rebalances the portfolio to achieve a good balance between expected risk (variance) $x^\top \Sigma x$ and returns $\mu^\top x$. In it's most simple form we want to solve:
\[\begin{array}{ll} \text{maximize} & \mu^\top x - \gamma (x^\top \Sigma x)\\ \text{subject to} & 1^\top x = d + 1^\top x^0 \\ & x \geq 0, \end{array}\]
with variable $x \in \mathbf{R}^n$, $\mu$ forecasted (expected) returns, $\gamma > 0 $ risk aversion parameter. $x^0_i$ represents the initial investment in asset $i$ and $d$ represents the cash reserve. Consequently, the equality constraint tells us that the sum of the new allocation vector $x$ has to equal the initial allocation plus the cash reserve. Furthermore, the covariance matrix of our risk model is given by $\Sigma \in \mathbf{S}_+^n$. Here we assume a factor risk model, i.e. we can write $\Sigma$ as $\Sigma = D + F F^\top$ where $D$ is diagonal and the factor matrix $F$ has a lower rank $k < n$. This approach allows us to reduce the number of nonzeros in the problem. Furthermore, note that we don't consider shortselling in this example. Let's generate some problem data:
using LinearAlgebra, SparseArrays, Random, COSMO, JuMP, Test
# generate the data
rng = Random.MersenneTwister(1)
k = 5; # number of factors
n = k * 10; # number of assets
D = spdiagm(0 => rand(rng, n) .* sqrt(k))
F = sprandn(rng, n, k, 0.5); # factor loading matrix
μ = (3 .+ 9. * rand(rng, n)) / 100. # expected returns between 3% - 12%
γ = 1.0; # risk aversion parameter
d = 1 # we are starting from all cash
x0 = zeros(n);We can now write the problem as a QP:
\[\begin{array}{ll} \text{minimize} & x^\top D x + y^\top y - \gamma^{-1} \mu^\top x \\ \text{subject to} & y = F^\top x \\ & 1^\top x = d + 1^\top x^0 \\ & x \geq 0. \end{array}\]
Before considering other effects, let's create the model in JuMP and solve it using COSMO:
model = JuMP.Model(COSMO.Optimizer);
@variable(model, x[1:n]);
@variable(model, y[1:k]);
@objective(model, Min, x' * D * x + y' * y - 1/γ * μ' * x);
@constraint(model, y .== F' * x);
@constraint(model, sum(x) == d + sum(x0));
@constraint(model, x .>= 0);
JuMP.optimize!(model)Minimize ScalarQuadraticFunction{Float64}:
0.0 - 0.03385565814267903 x[1] - 0.04590006304364081 x[2] - 0.03187675407487563 x[3] - 0.038643489330353845 x[4] - 0.11537394365293047 x[5] - 0.07843124729674311 x[6] - 0.1061249327667408 x[7] - 0.10449408892289712 x[8] - 0.06113876921991911 x[9] - 0.061720440636723016 x[10] - 0.07772536451186118 x[11] - 0.08479052793558062 x[12] - 0.034173154942416295 x[13] - 0.10986303487154454 x[14] - 0.06494086085801082 x[15] - 0.06794986796998538 x[16] - 0.09660389740328687 x[17] - 0.11664450096167028 x[18] - 0.04025890560946719 x[19] - 0.07245375681407701 x[20] - 0.06273656986263487 x[21] - 0.0790698498853181 x[22] - 0.07719816805893663 x[23] - 0.060797530277889915 x[24] - 0.09186174293751685 x[25] - 0.054561528519170184 x[26] - 0.06353228073856151 x[27] - 0.11090748443468627 x[28] - 0.11926048788677207 x[29] - 0.10268917857414 x[30] - 0.0978743820799869 x[31] - 0.11162836887357093 x[32] - 0.09964056132213991 x[33] - 0.0814858917162367 x[34] - 0.03397713731387059 x[35] - 0.06339040606049569 x[36] - 0.07826350307098548 x[37] - 0.042251188947556806 x[38] - 0.06285561950168692 x[39] - 0.03933137671410103 x[40] - 0.0964384127188235 x[41] - 0.053999573566858555 x[42] - 0.07602434742374685 x[43] - 0.042312459588649445 x[44] - 0.03386125813757613 x[45] - 0.11841905497987099 x[46] - 0.09816561459529043 x[47] - 0.07174408363301076 x[48] - 0.050537781372324536 x[49] - 0.06455521149980631 x[50] + 1.0 y[1]² + 1.0 y[2]² + 1.0 y[3]² + 1.0 y[4]² + 1.0 y[5]² + 0.22168311155166154 x[1]² + 1.569674359079319 x[2]² + 1.1253275636203313 x[3]² + 1.958440472561891 x[4]² + 2.1320134751461897 x[5]² + 1.1354989565743618 x[6]² + 1.7659372870351717 x[7]² + 0.1593290841959982 x[8]² + 0.3094227911776114 x[9]² + 0.8791977343224676 x[10]² + 0.39742223612651667 x[11]² + 1.8875918586267313 x[12]² + 1.8387120048986592 x[13]² + 2.190053109789465 x[14]² + 2.1957255604735644 x[15]² + 2.1978762529481384 x[16]² + 1.1710828933547 x[17]² + 1.2987007815595075 x[18]² + 0.281209441224692 x[19]² + 0.33479111624495367 x[20]² + 1.8966897412188368 x[21]² + 1.401948599916701 x[22]² + 2.160159812386103 x[23]² + 1.9353413223067184 x[24]² + 1.8453446813850807 x[25]² + 0.5624261051786525 x[26]² + 1.0198781850630045 x[27]² + 2.0113520898601918 x[28]² + 1.4681359454446885 x[29]² + 0.5963127696051644 x[30]² + 0.5175042820439373 x[31]² + 1.852649196595403 x[32]² + 1.8159596121340185 x[33]² + 0.6715708566047849 x[34]² + 0.546141819204228 x[35]² + 1.7261425935764683 x[36]² + 1.8841597069654406 x[37]² + 1.8282514435305761 x[38]² + 1.9568900128195392 x[39]² + 1.9503256911912632 x[40]² + 1.0526772112820373 x[41]² + 1.0229536502198167 x[42]² + 0.8792148153431698 x[43]² + 2.1254116542837194 x[44]² + 1.7521275518465191 x[45]² + 1.4534148949272803 x[46]² + 0.2944245797695367 x[47]² + 0.2754584682030851 x[48]² + 0.43199283796505494 x[49]² + 2.0761956200923155 x[50]²
Subject to:
VectorAffineFunction{Float64}-in-Zeros
┌ ┐
│0.0 - 0.45836571560595957 x[1] - 1.4882021641049918 x[2] + 2.1826127685114023 x[4] + 0.8239262467380715 x[6] - 1.2962721783934823 x[9] + 0.19983857542320999 x[11] - 1.435940970672912 x[13] + 1.194939742800976 x[18] - 0.7605416579955722 x[19] - 0.10198063634911336 x[20] + 0.0962615513861198 x[23] - 0.12018274708623239 x[26] - 0.7295613191446634 x[27] - 0.07270642655012116 x[28] - 0.8907108705599415 x[29] - 1.0051237161319388 x[30] - 0.8232754710476714 x[31] - 0.3127161299324051 x[32] - 0.7795842203334354 x[34] + 0.9216601059658592 x[35] - 2.069856046894368 x[36] - 0.5189602133669754 x[37] + 0.5885760717502199 x[38] - 0.7196314555287213 x[40] - 0.9291963494383236 x[43] - 0.17796544541790937 x[44] + 0.41792527291699105 x[45] + 0.5159420767895866 x[48] + 1.0 y[1]│
└ ┘ ∈ Zeros(1)
┌ ┐
│0.0 + 0.0503378286805425 x[4] + 1.1256748837213493 x[6] + 0.7658960317180369 x[8] - 0.061035008743322475 x[10] + 0.6046067312789892 x[11] + 1.683500023265881 x[12] + 1.201178638729371 x[13] + 0.6155732499801082 x[14] + 2.4402033735474125 x[23] - 0.7379012770819809 x[24] + 0.20489758707586392 x[25] + 1.2320869079191876 x[26] - 1.9402369852338388 x[27] - 0.954777195400799 x[31] - 0.344798870223836 x[32] + 0.17805576280533475 x[34] + 0.24224089365318544 x[37] - 1.7590069644534676 x[38] + 1.4165151237242104 x[40] + 0.8808123403489245 x[43] - 0.4474817348974519 x[44] + 0.8136739930455366 x[45] + 0.997384476726562 x[47] + 1.0 y[2]│
└ ┘ ∈ Zeros(1)
┌ ┐
│0.0 - 0.20209121321144838 x[1] + 1.157104812420386 x[2] + 0.45265959148235724 x[3] - 0.8009036795569376 x[4] - 2.0302615696038253 x[5] + 0.6241037854724422 x[6] + 0.8271047378482009 x[12] - 1.8249637555191254 x[14] + 0.054713116051507256 x[15] + 1.1115572615284857 x[17] + 1.7828304776409556 x[18] + 0.7423713791628864 x[19] + 0.5552255444433157 x[21] + 0.2303118558750502 x[22] + 0.10973142914455558 x[23] - 0.16181023670093883 x[25] + 1.7265600749058716 x[26] + 1.0154508128378734 x[30] - 0.9272881543745629 x[32] - 0.8528545030926377 x[34] - 0.8887796114735067 x[35] - 0.6372939953316094 x[37] - 2.0729975098289883 x[38] + 0.21793972328895084 x[39] + 0.5968016554494258 x[40] + 0.8446725934201121 x[41] - 0.6564960898033011 x[42] - 0.2577617922174006 x[45] + 1.6066125045474893 x[47] - 0.6106753315638065 x[49] - 0.24094934017892947 x[50] + 1.0 y[3]│
└ ┘ ∈ Zeros(1)
┌ ┐
│0.0 + 0.24314199505818793 x[2] - 1.3876541437893315 x[4] - 0.22683790735634463 x[6] + 0.5214802680235079 x[7] + 1.3354590673591633 x[8] - 1.8504774775149704 x[9] + 0.23051379143328576 x[13] - 0.1572785018821299 x[14] - 1.483039278741509 x[15] - 0.26226284250578463 x[16] - 0.0986696994672989 x[17] - 0.08550126212770054 x[20] + 0.3419778094275683 x[22] + 0.06543821802916351 x[23] - 0.2207564607343709 x[25] - 0.6273452593617963 x[26] + 0.37311820250796757 x[27] - 1.1054210865179164 x[28] + 0.5615671906319677 x[29] - 0.1030742062121358 x[30] - 0.13774215623815417 x[31] + 0.4839037548487663 x[33] + 0.8926885669157067 x[34] - 2.5405468288052515 x[35] + 0.2874685755965493 x[36] - 0.23047583769083854 x[39] + 1.1096979208454745 x[40] + 1.3964654491745603 x[44] - 0.5374828725846994 x[45] + 1.4520935910396786 x[47] + 1.0 y[4]│
└ ┘ ∈ Zeros(1)
┌ ┐
│0.0 - 1.4139342679089253 x[1] - 0.35072192922287954 x[5] + 1.652168425225477 x[7] - 0.049113526881893764 x[18] - 0.8682023381498042 x[22] - 1.5204662064824461 x[23] - 1.3700941514175726 x[24] + 0.05398461169426838 x[25] + 0.013219813753395412 x[26] - 0.8595562201704314 x[31] + 2.3073642877859806 x[33] + 0.0566217713770541 x[35] + 0.12661760952546483 x[40] + 1.4067743147522846 x[41] - 1.2155494239575593 x[43] - 0.24750058660020918 x[47] - 1.7920247650821086 x[49] + 1.0 y[5]│
└ ┘ ∈ Zeros(1)
┌ ┐
│-1.0 + 1.0 x[1] + 1.0 x[2] + 1.0 x[3] + 1.0 x[4] + 1.0 x[5] + 1.0 x[6] + 1.0 x[7] + 1.0 x[8] + 1.0 x[9] + 1.0 x[10] + 1.0 x[11] + 1.0 x[12] + 1.0 x[13] + 1.0 x[14] + 1.0 x[15] + 1.0 x[16] + 1.0 x[17] + 1.0 x[18] + 1.0 x[19] + 1.0 x[20] + 1.0 x[21] + 1.0 x[22] + 1.0 x[23] + 1.0 x[24] + 1.0 x[25] + 1.0 x[26] + 1.0 x[27] + 1.0 x[28] + 1.0 x[29] + 1.0 x[30] + 1.0 x[31] + 1.0 x[32] + 1.0 x[33] + 1.0 x[34] + 1.0 x[35] + 1.0 x[36] + 1.0 x[37] + 1.0 x[38] + 1.0 x[39] + 1.0 x[40] + 1.0 x[41] + 1.0 x[42] + 1.0 x[43] + 1.0 x[44] + 1.0 x[45] + 1.0 x[46] + 1.0 x[47] + 1.0 x[48] + 1.0 x[49] + 1.0 x[50]│
└ ┘ ∈ Zeros(1)
VectorAffineFunction{Float64}-in-Nonnegatives
┌ ┐
│0.0 + 1.0 x[1]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[2]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[3]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[4]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[5]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[6]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[7]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[8]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[9]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[10]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[11]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[12]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[13]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[14]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[15]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[16]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[17]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[18]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[19]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[20]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[21]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[22]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[23]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[24]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[25]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[26]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[27]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[28]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[29]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[30]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[31]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[32]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[33]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[34]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[35]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[36]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[37]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[38]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[39]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[40]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[41]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[42]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[43]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[44]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[45]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[46]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[47]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[48]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[49]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[50]│
└ ┘ ∈ Nonnegatives(1)
------------------------------------------------------------------
COSMO v0.8.10 - A Quadratic Objective Conic Solver
Michael Garstka
University of Oxford, 2017 - 2022
------------------------------------------------------------------
Problem: x ∈ R^{55},
constraints: A ∈ R^{56x55} (234 nnz),
matrix size to factor: 111x111,
Floating-point precision: Float64
Sets: Nonnegatives of dim: 50
ZeroSet of dim: 6
Settings: ϵ_abs = 1.0e-05, ϵ_rel = 1.0e-05,
ϵ_prim_inf = 1.0e-04, ϵ_dual_inf = 1.0e-04,
ρ = 0.1, σ = 1e-06, α = 1.6,
max_iter = 5000,
scaling iter = 10 (on),
check termination every 25 iter,
check infeasibility every 40 iter,
KKT system solver: QDLDL
Acc: Anderson Type2{QRDecomp},
Memory size = 15, RestartedMemory,
Safeguarded: true, tol: 2.0
Setup Time: 0.23ms
Iter: Objective: Primal Res: Dual Res: Rho:
1 -7.1996e-02 6.0083e-01 6.2240e-02 1.0000e-01
25 -6.0123e-02 4.4659e-07 4.4564e-08 1.0000e-01
------------------------------------------------------------------
>>> Results
Status: Solved
Iterations: 31 (incl. 6 safeguarding iter)
Optimal objective: -0.06012
Runtime: 0.001s (0.64ms)After solving the problem, we can calculate the expected return and risk $\sigma= \sqrt{x^{* \top} \Sigma x^*}$:
x_opt = JuMP.value.(x);
y_opt = JuMP.value.(y);
expected_return_basic = dot(μ, x_opt)0.08591907576098547expected_risk_basic = sqrt(dot(y_opt, y_opt))0.016711399332736566Using standard deviation in the model
It is pointed out in [1] that above problem formulation can lead to numerical problems, e.g. if $\Sigma$ is not strictly positive semidefinite. Another option is to formulate the risk constraint in terms of the standard deviation $\|M^\top x \|$ where $M M^\top = D + F F^\top$ and bound it using a second-order cone constraint:
\[\begin{array}{ll} \text{minimize} & - \mu^\top x \\ \text{subject to} & \|M^\top x\| \leq \gamma \\ & 1^\top x = d + 1^\top x^0 \\ & x \geq 0. \end{array}\]
Mt = [D.^0.5; F']
model = JuMP.Model(COSMO.Optimizer);
@variable(model, x[1:n]);
@objective(model, Min, - μ' * x);
@constraint(model, [γ; Mt * x] in SecondOrderCone()); # ||M'x|| <= γ
@constraint(model, sum(x) == d + sum(x0));
@constraint(model, x .>= 0);
JuMP.optimize!(model)Minimize ScalarAffineFunction{Float64}:
0.0 - 0.03385565814267903 x[1] - 0.04590006304364081 x[2] - 0.03187675407487563 x[3] - 0.038643489330353845 x[4] - 0.11537394365293047 x[5] - 0.07843124729674311 x[6] - 0.1061249327667408 x[7] - 0.10449408892289712 x[8] - 0.06113876921991911 x[9] - 0.061720440636723016 x[10] - 0.07772536451186118 x[11] - 0.08479052793558062 x[12] - 0.034173154942416295 x[13] - 0.10986303487154454 x[14] - 0.06494086085801082 x[15] - 0.06794986796998538 x[16] - 0.09660389740328687 x[17] - 0.11664450096167028 x[18] - 0.04025890560946719 x[19] - 0.07245375681407701 x[20] - 0.06273656986263487 x[21] - 0.0790698498853181 x[22] - 0.07719816805893663 x[23] - 0.060797530277889915 x[24] - 0.09186174293751685 x[25] - 0.054561528519170184 x[26] - 0.06353228073856151 x[27] - 0.11090748443468627 x[28] - 0.11926048788677207 x[29] - 0.10268917857414 x[30] - 0.0978743820799869 x[31] - 0.11162836887357093 x[32] - 0.09964056132213991 x[33] - 0.0814858917162367 x[34] - 0.03397713731387059 x[35] - 0.06339040606049569 x[36] - 0.07826350307098548 x[37] - 0.042251188947556806 x[38] - 0.06285561950168692 x[39] - 0.03933137671410103 x[40] - 0.0964384127188235 x[41] - 0.053999573566858555 x[42] - 0.07602434742374685 x[43] - 0.042312459588649445 x[44] - 0.03386125813757613 x[45] - 0.11841905497987099 x[46] - 0.09816561459529043 x[47] - 0.07174408363301076 x[48] - 0.050537781372324536 x[49] - 0.06455521149980631 x[50]
Subject to:
VectorAffineFunction{Float64}-in-Zeros
┌ ┐
│-1.0 + 1.0 x[1] + 1.0 x[2] + 1.0 x[3] + 1.0 x[4] + 1.0 x[5] + 1.0 x[6] + 1.0 x[7] + 1.0 x[8] + 1.0 x[9] + 1.0 x[10] + 1.0 x[11] + 1.0 x[12] + 1.0 x[13] + 1.0 x[14] + 1.0 x[15] + 1.0 x[16] + 1.0 x[17] + 1.0 x[18] + 1.0 x[19] + 1.0 x[20] + 1.0 x[21] + 1.0 x[22] + 1.0 x[23] + 1.0 x[24] + 1.0 x[25] + 1.0 x[26] + 1.0 x[27] + 1.0 x[28] + 1.0 x[29] + 1.0 x[30] + 1.0 x[31] + 1.0 x[32] + 1.0 x[33] + 1.0 x[34] + 1.0 x[35] + 1.0 x[36] + 1.0 x[37] + 1.0 x[38] + 1.0 x[39] + 1.0 x[40] + 1.0 x[41] + 1.0 x[42] + 1.0 x[43] + 1.0 x[44] + 1.0 x[45] + 1.0 x[46] + 1.0 x[47] + 1.0 x[48] + 1.0 x[49] + 1.0 x[50]│
└ ┘ ∈ Zeros(1)
VectorAffineFunction{Float64}-in-Nonnegatives
┌ ┐
│0.0 + 1.0 x[1]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[2]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[3]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[4]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[5]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[6]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[7]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[8]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[9]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[10]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[11]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[12]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[13]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[14]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[15]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[16]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[17]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[18]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[19]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[20]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[21]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[22]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[23]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[24]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[25]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[26]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[27]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[28]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[29]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[30]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[31]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[32]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[33]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[34]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[35]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[36]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[37]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[38]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[39]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[40]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[41]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[42]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[43]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[44]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[45]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[46]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[47]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[48]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[49]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[50]│
└ ┘ ∈ Nonnegatives(1)
VectorAffineFunction{Float64}-in-SecondOrderCone
┌ ┐
│1.0 │
│0.0 + 0.47083236034884174 x[1] │
│0.0 + 1.2528664570014312 x[2] │
│0.0 + 1.0608145755127667 x[3] │
│0.0 + 1.3994429150779573 x[4] │
│0.0 + 1.4601415942113936 x[5] │
│0.0 + 1.065597933826057 x[6] │
│0.0 + 1.3288857313686424 x[7] │
│0.0 + 0.3991604742406219 x[8] │
│0.0 + 0.5562578459470136 x[9] │
│0.0 + 0.9376554454182344 x[10] │
│0.0 + 0.6304143368662524 x[11] │
│0.0 + 1.373896596773837 x[12] │
│0.0 + 1.3559911522199026 x[13] │
│0.0 + 1.4798828027210347 x[14] │
│0.0 + 1.4817980835706208 x[15] │
│0.0 + 1.4825236095752872 x[16] │
│0.0 + 1.0821658344979757 x[17] │
│0.0 + 1.1396055377013168 x[18] │
│0.0 + 0.530291845331127 x[19] │
│0.0 + 0.5786113689212766 x[20] │
│0.0 + 1.3772035946870154 x[21] │
│0.0 + 1.1840391040488067 x[22] │
│0.0 + 1.4697482139421374 x[23] │
│0.0 + 1.3911654546842078 x[24] │
│0.0 + 1.3584346437665231 x[25] │
│0.0 + 0.7499507351677526 x[26] │
│0.0 + 1.0098901846552448 x[27] │
│0.0 + 1.4182214530390491 x[28] │
│0.0 + 1.2116665983036292 x[29] │
│0.0 + 0.7722129043244256 x[30] │
│0.0 + 0.7193777047170264 x[31] │
│0.0 + 1.3611205665169428 x[32] │
│0.0 + 1.3475754569351648 x[33] │
│0.0 + 0.8194942688053315 x[34] │
│0.0 + 0.7390140859308624 x[35] │
│0.0 + 1.313827459591429 x[36] │
│0.0 + 1.3726469709890596 x[37] │
│0.0 + 1.3521284863246452 x[38] │
│0.0 + 1.3988888493441998 x[39] │
│0.0 + 1.3965406156611642 x[40] │
│0.0 + 1.0260005902932208 x[41] │
│0.0 + 1.0114117115298877 x[42] │
│0.0 + 0.9376645537414592 x[43] │
│0.0 + 1.4578791631283161 x[44] │
│0.0 + 1.3236795502864427 x[45] │
│0.0 + 1.2055765819421345 x[46] │
│0.0 + 0.542609048735401 x[47] │
│0.0 + 0.5248413743247431 x[48] │
│0.0 + 0.6572616206390381 x[49] │
│0.0 + 1.4409009751167203 x[50] │
│0.0 + 0.45836571560595957 x[1] + 1.4882021641049918 x[2] - 2.1826127685114023 x[4] - 0.8239262467380715 x[6] + 1.2962721783934823 x[9] - 0.19983857542320999 x[11] + 1.435940970672912 x[13] - 1.194939742800976 x[18] + 0.7605416579955722 x[19] + 0.10198063634911336 x[20] - 0.0962615513861198 x[23] + 0.12018274708623239 x[26] + 0.7295613191446634 x[27] + 0.07270642655012116 x[28] + 0.8907108705599415 x[29] + 1.0051237161319388 x[30] + 0.8232754710476714 x[31] + 0.3127161299324051 x[32] + 0.7795842203334354 x[34] - 0.9216601059658592 x[35] + 2.069856046894368 x[36] + 0.5189602133669754 x[37] - 0.5885760717502199 x[38] + 0.7196314555287213 x[40] + 0.9291963494383236 x[43] + 0.17796544541790937 x[44] - 0.41792527291699105 x[45] - 0.5159420767895866 x[48] │
│0.0 - 0.0503378286805425 x[4] - 1.1256748837213493 x[6] - 0.7658960317180369 x[8] + 0.061035008743322475 x[10] - 0.6046067312789892 x[11] - 1.683500023265881 x[12] - 1.201178638729371 x[13] - 0.6155732499801082 x[14] - 2.4402033735474125 x[23] + 0.7379012770819809 x[24] - 0.20489758707586392 x[25] - 1.2320869079191876 x[26] + 1.9402369852338388 x[27] + 0.954777195400799 x[31] + 0.344798870223836 x[32] - 0.17805576280533475 x[34] - 0.24224089365318544 x[37] + 1.7590069644534676 x[38] - 1.4165151237242104 x[40] - 0.8808123403489245 x[43] + 0.4474817348974519 x[44] - 0.8136739930455366 x[45] - 0.997384476726562 x[47] │
│0.0 + 0.20209121321144838 x[1] - 1.157104812420386 x[2] - 0.45265959148235724 x[3] + 0.8009036795569376 x[4] + 2.0302615696038253 x[5] - 0.6241037854724422 x[6] - 0.8271047378482009 x[12] + 1.8249637555191254 x[14] - 0.054713116051507256 x[15] - 1.1115572615284857 x[17] - 1.7828304776409556 x[18] - 0.7423713791628864 x[19] - 0.5552255444433157 x[21] - 0.2303118558750502 x[22] - 0.10973142914455558 x[23] + 0.16181023670093883 x[25] - 1.7265600749058716 x[26] - 1.0154508128378734 x[30] + 0.9272881543745629 x[32] + 0.8528545030926377 x[34] + 0.8887796114735067 x[35] + 0.6372939953316094 x[37] + 2.0729975098289883 x[38] - 0.21793972328895084 x[39] - 0.5968016554494258 x[40] - 0.8446725934201121 x[41] + 0.6564960898033011 x[42] + 0.2577617922174006 x[45] - 1.6066125045474893 x[47] + 0.6106753315638065 x[49] + 0.24094934017892947 x[50]│
│0.0 - 0.24314199505818793 x[2] + 1.3876541437893315 x[4] + 0.22683790735634463 x[6] - 0.5214802680235079 x[7] - 1.3354590673591633 x[8] + 1.8504774775149704 x[9] - 0.23051379143328576 x[13] + 0.1572785018821299 x[14] + 1.483039278741509 x[15] + 0.26226284250578463 x[16] + 0.0986696994672989 x[17] + 0.08550126212770054 x[20] - 0.3419778094275683 x[22] - 0.06543821802916351 x[23] + 0.2207564607343709 x[25] + 0.6273452593617963 x[26] - 0.37311820250796757 x[27] + 1.1054210865179164 x[28] - 0.5615671906319677 x[29] + 0.1030742062121358 x[30] + 0.13774215623815417 x[31] - 0.4839037548487663 x[33] - 0.8926885669157067 x[34] + 2.5405468288052515 x[35] - 0.2874685755965493 x[36] + 0.23047583769083854 x[39] - 1.1096979208454745 x[40] - 1.3964654491745603 x[44] + 0.5374828725846994 x[45] - 1.4520935910396786 x[47] │
│0.0 + 1.4139342679089253 x[1] + 0.35072192922287954 x[5] - 1.652168425225477 x[7] + 0.049113526881893764 x[18] + 0.8682023381498042 x[22] + 1.5204662064824461 x[23] + 1.3700941514175726 x[24] - 0.05398461169426838 x[25] - 0.013219813753395412 x[26] + 0.8595562201704314 x[31] - 2.3073642877859806 x[33] - 0.0566217713770541 x[35] - 0.12661760952546483 x[40] - 1.4067743147522846 x[41] + 1.2155494239575593 x[43] + 0.24750058660020918 x[47] + 1.7920247650821086 x[49] │
└ ┘ ∈ SecondOrderCone(56)
------------------------------------------------------------------
COSMO v0.8.10 - A Quadratic Objective Conic Solver
Michael Garstka
University of Oxford, 2017 - 2022
------------------------------------------------------------------
Problem: x ∈ R^{50},
constraints: A ∈ R^{107x50} (279 nnz),
matrix size to factor: 157x157,
Floating-point precision: Float64
Sets: SecondOrderCone of dim: 56
Nonnegatives of dim: 50
ZeroSet of dim: 1
Settings: ϵ_abs = 1.0e-05, ϵ_rel = 1.0e-05,
ϵ_prim_inf = 1.0e-04, ϵ_dual_inf = 1.0e-04,
ρ = 0.1, σ = 1e-06, α = 1.6,
max_iter = 5000,
scaling iter = 10 (on),
check termination every 25 iter,
check infeasibility every 40 iter,
KKT system solver: QDLDL
Acc: Anderson Type2{QRDecomp},
Memory size = 15, RestartedMemory,
Safeguarded: true, tol: 2.0
Setup Time: 0.32ms
Iter: Objective: Primal Res: Dual Res: Rho:
1 -2.8909e-01 6.0109e-01 6.1889e-02 1.0000e-01
25 -1.1753e-01 5.6656e-03 5.4622e-03 1.0000e-01
50 -1.1821e-01 6.6171e-04 2.5383e-03 1.0000e-01
75 -1.1943e-01 1.3526e-02 3.7204e-03 1.0000e-01
100 -1.1585e-01 9.0860e-03 5.0601e-04 9.7648e-03
125 -1.1724e-01 1.8421e-03 1.7005e-04 9.7648e-03
150 -1.1894e-01 1.0337e-04 1.0152e-05 9.7648e-03
175 -1.1883e-01 7.8719e-06 2.2639e-07 9.7648e-03
------------------------------------------------------------------
>>> Results
Status: Solved
Iterations: 183 (incl. 8 safeguarding iter)
Optimal objective: -0.1188
Runtime: 0.005s (5.17ms)Note that the result is different from the example above because $\gamma$ scales the problem in a different way. Here it can be seen as an upper bound on the standard deviation of the portfolio.
x_opt = JuMP.value.(x);
expected_return = dot(μ, x_opt)0.11882650366846392Let us verify that the bound holds:
@test norm(Mt * x_opt) <= γTest PassedPareto-optimal front
The above portfolio optimisation approach yields the optimal expected return for a given level of risk. The result is obviously impacted by the risk aversion $\gamma$ parameter. To visualise the trade-off and present the investor with an efficient Pareto optimal portfolio for their risk appetite we can compute the optimal portfolio for many choices of $\gamma$ and plot the corresponding risk-return trade-off curve.
gammas = [ 0.001, 0.01, 0.1, 0.5, 1., 3., 10, 100, 1000]
risks = zeros(length(gammas))
returns = zeros(length(gammas))
model = JuMP.Model(optimizer_with_attributes(COSMO.Optimizer, "verbose" => false));
@variable(model, x[1:n]);
@variable(model, y[1:k]);
@objective(model, Min, x' * D * x + y' * y - 1/γ * μ' * x);
@constraint(model, y .== F' * x);
@constraint(model, sum(x) == d + sum(x0));
@constraint(model, x .>= 0);
# solve the same problem for different values of γ
for (k, gamma) in enumerate(gammas)
coeff = - 1/gamma * μ
JuMP.set_objective_coefficient.(model, x, coeff)
JuMP.optimize!(model)
local x_opt = JuMP.value.(x);
local y_opt = JuMP.value.(y);
returns[k] = dot(μ, x_opt)
risks[k] = sqrt(dot(y_opt, y_opt))
endMinimize ScalarQuadraticFunction{Float64}:
0.0 - 33.85565814267903 x[1] - 45.90006304364081 x[2] - 31.876754074875628 x[3] - 38.643489330353844 x[4] - 115.37394365293046 x[5] - 78.43124729674311 x[6] - 106.1249327667408 x[7] - 104.49408892289712 x[8] - 61.13876921991911 x[9] - 61.72044063672302 x[10] - 77.72536451186119 x[11] - 84.79052793558061 x[12] - 34.173154942416296 x[13] - 109.86303487154454 x[14] - 64.94086085801082 x[15] - 67.94986796998538 x[16] - 96.60389740328687 x[17] - 116.64450096167029 x[18] - 40.25890560946719 x[19] - 72.45375681407701 x[20] - 62.73656986263487 x[21] - 79.06984988531809 x[22] - 77.19816805893663 x[23] - 60.79753027788991 x[24] - 91.86174293751685 x[25] - 54.56152851917018 x[26] - 63.53228073856151 x[27] - 110.90748443468627 x[28] - 119.26048788677207 x[29] - 102.68917857414 x[30] - 97.8743820799869 x[31] - 111.62836887357093 x[32] - 99.64056132213992 x[33] - 81.4858917162367 x[34] - 33.977137313870585 x[35] - 63.390406060495685 x[36] - 78.26350307098548 x[37] - 42.251188947556805 x[38] - 62.85561950168692 x[39] - 39.331376714101026 x[40] - 96.4384127188235 x[41] - 53.99957356685856 x[42] - 76.02434742374685 x[43] - 42.312459588649446 x[44] - 33.86125813757613 x[45] - 118.41905497987099 x[46] - 98.16561459529042 x[47] - 71.74408363301076 x[48] - 50.53778137232454 x[49] - 64.5552114998063 x[50] + 1.0 y[1]² + 1.0 y[2]² + 1.0 y[3]² + 1.0 y[4]² + 1.0 y[5]² + 0.22168311155166154 x[1]² + 1.569674359079319 x[2]² + 1.1253275636203313 x[3]² + 1.958440472561891 x[4]² + 2.1320134751461897 x[5]² + 1.1354989565743618 x[6]² + 1.7659372870351717 x[7]² + 0.1593290841959982 x[8]² + 0.3094227911776114 x[9]² + 0.8791977343224676 x[10]² + 0.39742223612651667 x[11]² + 1.8875918586267313 x[12]² + 1.8387120048986592 x[13]² + 2.190053109789465 x[14]² + 2.1957255604735644 x[15]² + 2.1978762529481384 x[16]² + 1.1710828933547 x[17]² + 1.2987007815595075 x[18]² + 0.281209441224692 x[19]² + 0.33479111624495367 x[20]² + 1.8966897412188368 x[21]² + 1.401948599916701 x[22]² + 2.160159812386103 x[23]² + 1.9353413223067184 x[24]² + 1.8453446813850807 x[25]² + 0.5624261051786525 x[26]² + 1.0198781850630045 x[27]² + 2.0113520898601918 x[28]² + 1.4681359454446885 x[29]² + 0.5963127696051644 x[30]² + 0.5175042820439373 x[31]² + 1.852649196595403 x[32]² + 1.8159596121340185 x[33]² + 0.6715708566047849 x[34]² + 0.546141819204228 x[35]² + 1.7261425935764683 x[36]² + 1.8841597069654406 x[37]² + 1.8282514435305761 x[38]² + 1.9568900128195392 x[39]² + 1.9503256911912632 x[40]² + 1.0526772112820373 x[41]² + 1.0229536502198167 x[42]² + 0.8792148153431698 x[43]² + 2.1254116542837194 x[44]² + 1.7521275518465191 x[45]² + 1.4534148949272803 x[46]² + 0.2944245797695367 x[47]² + 0.2754584682030851 x[48]² + 0.43199283796505494 x[49]² + 2.0761956200923155 x[50]²
Subject to:
VectorAffineFunction{Float64}-in-Zeros
┌ ┐
│0.0 - 0.45836571560595957 x[1] - 1.4882021641049918 x[2] + 2.1826127685114023 x[4] + 0.8239262467380715 x[6] - 1.2962721783934823 x[9] + 0.19983857542320999 x[11] - 1.435940970672912 x[13] + 1.194939742800976 x[18] - 0.7605416579955722 x[19] - 0.10198063634911336 x[20] + 0.0962615513861198 x[23] - 0.12018274708623239 x[26] - 0.7295613191446634 x[27] - 0.07270642655012116 x[28] - 0.8907108705599415 x[29] - 1.0051237161319388 x[30] - 0.8232754710476714 x[31] - 0.3127161299324051 x[32] - 0.7795842203334354 x[34] + 0.9216601059658592 x[35] - 2.069856046894368 x[36] - 0.5189602133669754 x[37] + 0.5885760717502199 x[38] - 0.7196314555287213 x[40] - 0.9291963494383236 x[43] - 0.17796544541790937 x[44] + 0.41792527291699105 x[45] + 0.5159420767895866 x[48] + 1.0 y[1]│
└ ┘ ∈ Zeros(1)
┌ ┐
│0.0 + 0.0503378286805425 x[4] + 1.1256748837213493 x[6] + 0.7658960317180369 x[8] - 0.061035008743322475 x[10] + 0.6046067312789892 x[11] + 1.683500023265881 x[12] + 1.201178638729371 x[13] + 0.6155732499801082 x[14] + 2.4402033735474125 x[23] - 0.7379012770819809 x[24] + 0.20489758707586392 x[25] + 1.2320869079191876 x[26] - 1.9402369852338388 x[27] - 0.954777195400799 x[31] - 0.344798870223836 x[32] + 0.17805576280533475 x[34] + 0.24224089365318544 x[37] - 1.7590069644534676 x[38] + 1.4165151237242104 x[40] + 0.8808123403489245 x[43] - 0.4474817348974519 x[44] + 0.8136739930455366 x[45] + 0.997384476726562 x[47] + 1.0 y[2]│
└ ┘ ∈ Zeros(1)
┌ ┐
│0.0 - 0.20209121321144838 x[1] + 1.157104812420386 x[2] + 0.45265959148235724 x[3] - 0.8009036795569376 x[4] - 2.0302615696038253 x[5] + 0.6241037854724422 x[6] + 0.8271047378482009 x[12] - 1.8249637555191254 x[14] + 0.054713116051507256 x[15] + 1.1115572615284857 x[17] + 1.7828304776409556 x[18] + 0.7423713791628864 x[19] + 0.5552255444433157 x[21] + 0.2303118558750502 x[22] + 0.10973142914455558 x[23] - 0.16181023670093883 x[25] + 1.7265600749058716 x[26] + 1.0154508128378734 x[30] - 0.9272881543745629 x[32] - 0.8528545030926377 x[34] - 0.8887796114735067 x[35] - 0.6372939953316094 x[37] - 2.0729975098289883 x[38] + 0.21793972328895084 x[39] + 0.5968016554494258 x[40] + 0.8446725934201121 x[41] - 0.6564960898033011 x[42] - 0.2577617922174006 x[45] + 1.6066125045474893 x[47] - 0.6106753315638065 x[49] - 0.24094934017892947 x[50] + 1.0 y[3]│
└ ┘ ∈ Zeros(1)
┌ ┐
│0.0 + 0.24314199505818793 x[2] - 1.3876541437893315 x[4] - 0.22683790735634463 x[6] + 0.5214802680235079 x[7] + 1.3354590673591633 x[8] - 1.8504774775149704 x[9] + 0.23051379143328576 x[13] - 0.1572785018821299 x[14] - 1.483039278741509 x[15] - 0.26226284250578463 x[16] - 0.0986696994672989 x[17] - 0.08550126212770054 x[20] + 0.3419778094275683 x[22] + 0.06543821802916351 x[23] - 0.2207564607343709 x[25] - 0.6273452593617963 x[26] + 0.37311820250796757 x[27] - 1.1054210865179164 x[28] + 0.5615671906319677 x[29] - 0.1030742062121358 x[30] - 0.13774215623815417 x[31] + 0.4839037548487663 x[33] + 0.8926885669157067 x[34] - 2.5405468288052515 x[35] + 0.2874685755965493 x[36] - 0.23047583769083854 x[39] + 1.1096979208454745 x[40] + 1.3964654491745603 x[44] - 0.5374828725846994 x[45] + 1.4520935910396786 x[47] + 1.0 y[4]│
└ ┘ ∈ Zeros(1)
┌ ┐
│0.0 - 1.4139342679089253 x[1] - 0.35072192922287954 x[5] + 1.652168425225477 x[7] - 0.049113526881893764 x[18] - 0.8682023381498042 x[22] - 1.5204662064824461 x[23] - 1.3700941514175726 x[24] + 0.05398461169426838 x[25] + 0.013219813753395412 x[26] - 0.8595562201704314 x[31] + 2.3073642877859806 x[33] + 0.0566217713770541 x[35] + 0.12661760952546483 x[40] + 1.4067743147522846 x[41] - 1.2155494239575593 x[43] - 0.24750058660020918 x[47] - 1.7920247650821086 x[49] + 1.0 y[5]│
└ ┘ ∈ Zeros(1)
┌ ┐
│-1.0 + 1.0 x[1] + 1.0 x[2] + 1.0 x[3] + 1.0 x[4] + 1.0 x[5] + 1.0 x[6] + 1.0 x[7] + 1.0 x[8] + 1.0 x[9] + 1.0 x[10] + 1.0 x[11] + 1.0 x[12] + 1.0 x[13] + 1.0 x[14] + 1.0 x[15] + 1.0 x[16] + 1.0 x[17] + 1.0 x[18] + 1.0 x[19] + 1.0 x[20] + 1.0 x[21] + 1.0 x[22] + 1.0 x[23] + 1.0 x[24] + 1.0 x[25] + 1.0 x[26] + 1.0 x[27] + 1.0 x[28] + 1.0 x[29] + 1.0 x[30] + 1.0 x[31] + 1.0 x[32] + 1.0 x[33] + 1.0 x[34] + 1.0 x[35] + 1.0 x[36] + 1.0 x[37] + 1.0 x[38] + 1.0 x[39] + 1.0 x[40] + 1.0 x[41] + 1.0 x[42] + 1.0 x[43] + 1.0 x[44] + 1.0 x[45] + 1.0 x[46] + 1.0 x[47] + 1.0 x[48] + 1.0 x[49] + 1.0 x[50]│
└ ┘ ∈ Zeros(1)
VectorAffineFunction{Float64}-in-Nonnegatives
┌ ┐
│0.0 + 1.0 x[1]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[2]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[3]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[4]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[5]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[6]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[7]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[8]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[9]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[10]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[11]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[12]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[13]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[14]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[15]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[16]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[17]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[18]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[19]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[20]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[21]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[22]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[23]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[24]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[25]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[26]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[27]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[28]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[29]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[30]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[31]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[32]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[33]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[34]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[35]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[36]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[37]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[38]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[39]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[40]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[41]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[42]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[43]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[44]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[45]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[46]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[47]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[48]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[49]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[50]│
└ ┘ ∈ Nonnegatives(1)
Minimize ScalarQuadraticFunction{Float64}:
0.0 - 3.385565814267903 x[1] - 4.590006304364081 x[2] - 3.187675407487563 x[3] - 3.8643489330353846 x[4] - 11.537394365293046 x[5] - 7.843124729674312 x[6] - 10.61249327667408 x[7] - 10.449408892289712 x[8] - 6.113876921991912 x[9] - 6.172044063672302 x[10] - 7.772536451186118 x[11] - 8.479052793558061 x[12] - 3.4173154942416293 x[13] - 10.986303487154455 x[14] - 6.494086085801082 x[15] - 6.794986796998538 x[16] - 9.660389740328688 x[17] - 11.664450096167029 x[18] - 4.025890560946719 x[19] - 7.245375681407701 x[20] - 6.273656986263488 x[21] - 7.90698498853181 x[22] - 7.719816805893663 x[23] - 6.079753027788992 x[24] - 9.186174293751685 x[25] - 5.456152851917018 x[26] - 6.353228073856151 x[27] - 11.090748443468627 x[28] - 11.926048788677207 x[29] - 10.268917857414001 x[30] - 9.78743820799869 x[31] - 11.162836887357093 x[32] - 9.964056132213992 x[33] - 8.14858917162367 x[34] - 3.397713731387059 x[35] - 6.3390406060495685 x[36] - 7.826350307098548 x[37] - 4.22511889475568 x[38] - 6.285561950168692 x[39] - 3.933137671410103 x[40] - 9.64384127188235 x[41] - 5.399957356685856 x[42] - 7.602434742374685 x[43] - 4.231245958864944 x[44] - 3.386125813757613 x[45] - 11.8419054979871 x[46] - 9.816561459529042 x[47] - 7.174408363301075 x[48] - 5.053778137232453 x[49] - 6.455521149980631 x[50] + 1.0 y[1]² + 1.0 y[2]² + 1.0 y[3]² + 1.0 y[4]² + 1.0 y[5]² + 0.22168311155166154 x[1]² + 1.569674359079319 x[2]² + 1.1253275636203313 x[3]² + 1.958440472561891 x[4]² + 2.1320134751461897 x[5]² + 1.1354989565743618 x[6]² + 1.7659372870351717 x[7]² + 0.1593290841959982 x[8]² + 0.3094227911776114 x[9]² + 0.8791977343224676 x[10]² + 0.39742223612651667 x[11]² + 1.8875918586267313 x[12]² + 1.8387120048986592 x[13]² + 2.190053109789465 x[14]² + 2.1957255604735644 x[15]² + 2.1978762529481384 x[16]² + 1.1710828933547 x[17]² + 1.2987007815595075 x[18]² + 0.281209441224692 x[19]² + 0.33479111624495367 x[20]² + 1.8966897412188368 x[21]² + 1.401948599916701 x[22]² + 2.160159812386103 x[23]² + 1.9353413223067184 x[24]² + 1.8453446813850807 x[25]² + 0.5624261051786525 x[26]² + 1.0198781850630045 x[27]² + 2.0113520898601918 x[28]² + 1.4681359454446885 x[29]² + 0.5963127696051644 x[30]² + 0.5175042820439373 x[31]² + 1.852649196595403 x[32]² + 1.8159596121340185 x[33]² + 0.6715708566047849 x[34]² + 0.546141819204228 x[35]² + 1.7261425935764683 x[36]² + 1.8841597069654406 x[37]² + 1.8282514435305761 x[38]² + 1.9568900128195392 x[39]² + 1.9503256911912632 x[40]² + 1.0526772112820373 x[41]² + 1.0229536502198167 x[42]² + 0.8792148153431698 x[43]² + 2.1254116542837194 x[44]² + 1.7521275518465191 x[45]² + 1.4534148949272803 x[46]² + 0.2944245797695367 x[47]² + 0.2754584682030851 x[48]² + 0.43199283796505494 x[49]² + 2.0761956200923155 x[50]²
Subject to:
VectorAffineFunction{Float64}-in-Zeros
┌ ┐
│0.0 - 0.45836571560595957 x[1] - 1.4882021641049918 x[2] + 2.1826127685114023 x[4] + 0.8239262467380715 x[6] - 1.2962721783934823 x[9] + 0.19983857542320999 x[11] - 1.435940970672912 x[13] + 1.194939742800976 x[18] - 0.7605416579955722 x[19] - 0.10198063634911336 x[20] + 0.0962615513861198 x[23] - 0.12018274708623239 x[26] - 0.7295613191446634 x[27] - 0.07270642655012116 x[28] - 0.8907108705599415 x[29] - 1.0051237161319388 x[30] - 0.8232754710476714 x[31] - 0.3127161299324051 x[32] - 0.7795842203334354 x[34] + 0.9216601059658592 x[35] - 2.069856046894368 x[36] - 0.5189602133669754 x[37] + 0.5885760717502199 x[38] - 0.7196314555287213 x[40] - 0.9291963494383236 x[43] - 0.17796544541790937 x[44] + 0.41792527291699105 x[45] + 0.5159420767895866 x[48] + 1.0 y[1]│
└ ┘ ∈ Zeros(1)
┌ ┐
│0.0 + 0.0503378286805425 x[4] + 1.1256748837213493 x[6] + 0.7658960317180369 x[8] - 0.061035008743322475 x[10] + 0.6046067312789892 x[11] + 1.683500023265881 x[12] + 1.201178638729371 x[13] + 0.6155732499801082 x[14] + 2.4402033735474125 x[23] - 0.7379012770819809 x[24] + 0.20489758707586392 x[25] + 1.2320869079191876 x[26] - 1.9402369852338388 x[27] - 0.954777195400799 x[31] - 0.344798870223836 x[32] + 0.17805576280533475 x[34] + 0.24224089365318544 x[37] - 1.7590069644534676 x[38] + 1.4165151237242104 x[40] + 0.8808123403489245 x[43] - 0.4474817348974519 x[44] + 0.8136739930455366 x[45] + 0.997384476726562 x[47] + 1.0 y[2]│
└ ┘ ∈ Zeros(1)
┌ ┐
│0.0 - 0.20209121321144838 x[1] + 1.157104812420386 x[2] + 0.45265959148235724 x[3] - 0.8009036795569376 x[4] - 2.0302615696038253 x[5] + 0.6241037854724422 x[6] + 0.8271047378482009 x[12] - 1.8249637555191254 x[14] + 0.054713116051507256 x[15] + 1.1115572615284857 x[17] + 1.7828304776409556 x[18] + 0.7423713791628864 x[19] + 0.5552255444433157 x[21] + 0.2303118558750502 x[22] + 0.10973142914455558 x[23] - 0.16181023670093883 x[25] + 1.7265600749058716 x[26] + 1.0154508128378734 x[30] - 0.9272881543745629 x[32] - 0.8528545030926377 x[34] - 0.8887796114735067 x[35] - 0.6372939953316094 x[37] - 2.0729975098289883 x[38] + 0.21793972328895084 x[39] + 0.5968016554494258 x[40] + 0.8446725934201121 x[41] - 0.6564960898033011 x[42] - 0.2577617922174006 x[45] + 1.6066125045474893 x[47] - 0.6106753315638065 x[49] - 0.24094934017892947 x[50] + 1.0 y[3]│
└ ┘ ∈ Zeros(1)
┌ ┐
│0.0 + 0.24314199505818793 x[2] - 1.3876541437893315 x[4] - 0.22683790735634463 x[6] + 0.5214802680235079 x[7] + 1.3354590673591633 x[8] - 1.8504774775149704 x[9] + 0.23051379143328576 x[13] - 0.1572785018821299 x[14] - 1.483039278741509 x[15] - 0.26226284250578463 x[16] - 0.0986696994672989 x[17] - 0.08550126212770054 x[20] + 0.3419778094275683 x[22] + 0.06543821802916351 x[23] - 0.2207564607343709 x[25] - 0.6273452593617963 x[26] + 0.37311820250796757 x[27] - 1.1054210865179164 x[28] + 0.5615671906319677 x[29] - 0.1030742062121358 x[30] - 0.13774215623815417 x[31] + 0.4839037548487663 x[33] + 0.8926885669157067 x[34] - 2.5405468288052515 x[35] + 0.2874685755965493 x[36] - 0.23047583769083854 x[39] + 1.1096979208454745 x[40] + 1.3964654491745603 x[44] - 0.5374828725846994 x[45] + 1.4520935910396786 x[47] + 1.0 y[4]│
└ ┘ ∈ Zeros(1)
┌ ┐
│0.0 - 1.4139342679089253 x[1] - 0.35072192922287954 x[5] + 1.652168425225477 x[7] - 0.049113526881893764 x[18] - 0.8682023381498042 x[22] - 1.5204662064824461 x[23] - 1.3700941514175726 x[24] + 0.05398461169426838 x[25] + 0.013219813753395412 x[26] - 0.8595562201704314 x[31] + 2.3073642877859806 x[33] + 0.0566217713770541 x[35] + 0.12661760952546483 x[40] + 1.4067743147522846 x[41] - 1.2155494239575593 x[43] - 0.24750058660020918 x[47] - 1.7920247650821086 x[49] + 1.0 y[5]│
└ ┘ ∈ Zeros(1)
┌ ┐
│-1.0 + 1.0 x[1] + 1.0 x[2] + 1.0 x[3] + 1.0 x[4] + 1.0 x[5] + 1.0 x[6] + 1.0 x[7] + 1.0 x[8] + 1.0 x[9] + 1.0 x[10] + 1.0 x[11] + 1.0 x[12] + 1.0 x[13] + 1.0 x[14] + 1.0 x[15] + 1.0 x[16] + 1.0 x[17] + 1.0 x[18] + 1.0 x[19] + 1.0 x[20] + 1.0 x[21] + 1.0 x[22] + 1.0 x[23] + 1.0 x[24] + 1.0 x[25] + 1.0 x[26] + 1.0 x[27] + 1.0 x[28] + 1.0 x[29] + 1.0 x[30] + 1.0 x[31] + 1.0 x[32] + 1.0 x[33] + 1.0 x[34] + 1.0 x[35] + 1.0 x[36] + 1.0 x[37] + 1.0 x[38] + 1.0 x[39] + 1.0 x[40] + 1.0 x[41] + 1.0 x[42] + 1.0 x[43] + 1.0 x[44] + 1.0 x[45] + 1.0 x[46] + 1.0 x[47] + 1.0 x[48] + 1.0 x[49] + 1.0 x[50]│
└ ┘ ∈ Zeros(1)
VectorAffineFunction{Float64}-in-Nonnegatives
┌ ┐
│0.0 + 1.0 x[1]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[2]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[3]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[4]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[5]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[6]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[7]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[8]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[9]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[10]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[11]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[12]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[13]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[14]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[15]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[16]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[17]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[18]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[19]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[20]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[21]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[22]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[23]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[24]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[25]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[26]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[27]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[28]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[29]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[30]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[31]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[32]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[33]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[34]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[35]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[36]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[37]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[38]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[39]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[40]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[41]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[42]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[43]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[44]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[45]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[46]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[47]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[48]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[49]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[50]│
└ ┘ ∈ Nonnegatives(1)
Minimize ScalarQuadraticFunction{Float64}:
0.0 - 0.33855658142679035 x[1] - 0.4590006304364081 x[2] - 0.31876754074875624 x[3] - 0.3864348933035384 x[4] - 1.1537394365293046 x[5] - 0.7843124729674311 x[6] - 1.061249327667408 x[7] - 1.044940889228971 x[8] - 0.6113876921991911 x[9] - 0.6172044063672302 x[10] - 0.7772536451186118 x[11] - 0.8479052793558062 x[12] - 0.34173154942416295 x[13] - 1.0986303487154454 x[14] - 0.6494086085801082 x[15] - 0.6794986796998538 x[16] - 0.9660389740328688 x[17] - 1.166445009616703 x[18] - 0.4025890560946719 x[19] - 0.7245375681407701 x[20] - 0.6273656986263487 x[21] - 0.7906984988531809 x[22] - 0.7719816805893663 x[23] - 0.6079753027788991 x[24] - 0.9186174293751685 x[25] - 0.5456152851917019 x[26] - 0.6353228073856152 x[27] - 1.1090748443468628 x[28] - 1.1926048788677206 x[29] - 1.0268917857414 x[30] - 0.978743820799869 x[31] - 1.1162836887357093 x[32] - 0.9964056132213992 x[33] - 0.814858917162367 x[34] - 0.33977137313870587 x[35] - 0.6339040606049569 x[36] - 0.7826350307098549 x[37] - 0.42251188947556806 x[38] - 0.6285561950168692 x[39] - 0.3933137671410103 x[40] - 0.964384127188235 x[41] - 0.5399957356685856 x[42] - 0.7602434742374685 x[43] - 0.4231245958864944 x[44] - 0.3386125813757613 x[45] - 1.1841905497987097 x[46] - 0.9816561459529043 x[47] - 0.7174408363301076 x[48] - 0.5053778137232454 x[49] - 0.6455521149980631 x[50] + 1.0 y[1]² + 1.0 y[2]² + 1.0 y[3]² + 1.0 y[4]² + 1.0 y[5]² + 0.22168311155166154 x[1]² + 1.569674359079319 x[2]² + 1.1253275636203313 x[3]² + 1.958440472561891 x[4]² + 2.1320134751461897 x[5]² + 1.1354989565743618 x[6]² + 1.7659372870351717 x[7]² + 0.1593290841959982 x[8]² + 0.3094227911776114 x[9]² + 0.8791977343224676 x[10]² + 0.39742223612651667 x[11]² + 1.8875918586267313 x[12]² + 1.8387120048986592 x[13]² + 2.190053109789465 x[14]² + 2.1957255604735644 x[15]² + 2.1978762529481384 x[16]² + 1.1710828933547 x[17]² + 1.2987007815595075 x[18]² + 0.281209441224692 x[19]² + 0.33479111624495367 x[20]² + 1.8966897412188368 x[21]² + 1.401948599916701 x[22]² + 2.160159812386103 x[23]² + 1.9353413223067184 x[24]² + 1.8453446813850807 x[25]² + 0.5624261051786525 x[26]² + 1.0198781850630045 x[27]² + 2.0113520898601918 x[28]² + 1.4681359454446885 x[29]² + 0.5963127696051644 x[30]² + 0.5175042820439373 x[31]² + 1.852649196595403 x[32]² + 1.8159596121340185 x[33]² + 0.6715708566047849 x[34]² + 0.546141819204228 x[35]² + 1.7261425935764683 x[36]² + 1.8841597069654406 x[37]² + 1.8282514435305761 x[38]² + 1.9568900128195392 x[39]² + 1.9503256911912632 x[40]² + 1.0526772112820373 x[41]² + 1.0229536502198167 x[42]² + 0.8792148153431698 x[43]² + 2.1254116542837194 x[44]² + 1.7521275518465191 x[45]² + 1.4534148949272803 x[46]² + 0.2944245797695367 x[47]² + 0.2754584682030851 x[48]² + 0.43199283796505494 x[49]² + 2.0761956200923155 x[50]²
Subject to:
VectorAffineFunction{Float64}-in-Zeros
┌ ┐
│0.0 - 0.45836571560595957 x[1] - 1.4882021641049918 x[2] + 2.1826127685114023 x[4] + 0.8239262467380715 x[6] - 1.2962721783934823 x[9] + 0.19983857542320999 x[11] - 1.435940970672912 x[13] + 1.194939742800976 x[18] - 0.7605416579955722 x[19] - 0.10198063634911336 x[20] + 0.0962615513861198 x[23] - 0.12018274708623239 x[26] - 0.7295613191446634 x[27] - 0.07270642655012116 x[28] - 0.8907108705599415 x[29] - 1.0051237161319388 x[30] - 0.8232754710476714 x[31] - 0.3127161299324051 x[32] - 0.7795842203334354 x[34] + 0.9216601059658592 x[35] - 2.069856046894368 x[36] - 0.5189602133669754 x[37] + 0.5885760717502199 x[38] - 0.7196314555287213 x[40] - 0.9291963494383236 x[43] - 0.17796544541790937 x[44] + 0.41792527291699105 x[45] + 0.5159420767895866 x[48] + 1.0 y[1]│
└ ┘ ∈ Zeros(1)
┌ ┐
│0.0 + 0.0503378286805425 x[4] + 1.1256748837213493 x[6] + 0.7658960317180369 x[8] - 0.061035008743322475 x[10] + 0.6046067312789892 x[11] + 1.683500023265881 x[12] + 1.201178638729371 x[13] + 0.6155732499801082 x[14] + 2.4402033735474125 x[23] - 0.7379012770819809 x[24] + 0.20489758707586392 x[25] + 1.2320869079191876 x[26] - 1.9402369852338388 x[27] - 0.954777195400799 x[31] - 0.344798870223836 x[32] + 0.17805576280533475 x[34] + 0.24224089365318544 x[37] - 1.7590069644534676 x[38] + 1.4165151237242104 x[40] + 0.8808123403489245 x[43] - 0.4474817348974519 x[44] + 0.8136739930455366 x[45] + 0.997384476726562 x[47] + 1.0 y[2]│
└ ┘ ∈ Zeros(1)
┌ ┐
│0.0 - 0.20209121321144838 x[1] + 1.157104812420386 x[2] + 0.45265959148235724 x[3] - 0.8009036795569376 x[4] - 2.0302615696038253 x[5] + 0.6241037854724422 x[6] + 0.8271047378482009 x[12] - 1.8249637555191254 x[14] + 0.054713116051507256 x[15] + 1.1115572615284857 x[17] + 1.7828304776409556 x[18] + 0.7423713791628864 x[19] + 0.5552255444433157 x[21] + 0.2303118558750502 x[22] + 0.10973142914455558 x[23] - 0.16181023670093883 x[25] + 1.7265600749058716 x[26] + 1.0154508128378734 x[30] - 0.9272881543745629 x[32] - 0.8528545030926377 x[34] - 0.8887796114735067 x[35] - 0.6372939953316094 x[37] - 2.0729975098289883 x[38] + 0.21793972328895084 x[39] + 0.5968016554494258 x[40] + 0.8446725934201121 x[41] - 0.6564960898033011 x[42] - 0.2577617922174006 x[45] + 1.6066125045474893 x[47] - 0.6106753315638065 x[49] - 0.24094934017892947 x[50] + 1.0 y[3]│
└ ┘ ∈ Zeros(1)
┌ ┐
│0.0 + 0.24314199505818793 x[2] - 1.3876541437893315 x[4] - 0.22683790735634463 x[6] + 0.5214802680235079 x[7] + 1.3354590673591633 x[8] - 1.8504774775149704 x[9] + 0.23051379143328576 x[13] - 0.1572785018821299 x[14] - 1.483039278741509 x[15] - 0.26226284250578463 x[16] - 0.0986696994672989 x[17] - 0.08550126212770054 x[20] + 0.3419778094275683 x[22] + 0.06543821802916351 x[23] - 0.2207564607343709 x[25] - 0.6273452593617963 x[26] + 0.37311820250796757 x[27] - 1.1054210865179164 x[28] + 0.5615671906319677 x[29] - 0.1030742062121358 x[30] - 0.13774215623815417 x[31] + 0.4839037548487663 x[33] + 0.8926885669157067 x[34] - 2.5405468288052515 x[35] + 0.2874685755965493 x[36] - 0.23047583769083854 x[39] + 1.1096979208454745 x[40] + 1.3964654491745603 x[44] - 0.5374828725846994 x[45] + 1.4520935910396786 x[47] + 1.0 y[4]│
└ ┘ ∈ Zeros(1)
┌ ┐
│0.0 - 1.4139342679089253 x[1] - 0.35072192922287954 x[5] + 1.652168425225477 x[7] - 0.049113526881893764 x[18] - 0.8682023381498042 x[22] - 1.5204662064824461 x[23] - 1.3700941514175726 x[24] + 0.05398461169426838 x[25] + 0.013219813753395412 x[26] - 0.8595562201704314 x[31] + 2.3073642877859806 x[33] + 0.0566217713770541 x[35] + 0.12661760952546483 x[40] + 1.4067743147522846 x[41] - 1.2155494239575593 x[43] - 0.24750058660020918 x[47] - 1.7920247650821086 x[49] + 1.0 y[5]│
└ ┘ ∈ Zeros(1)
┌ ┐
│-1.0 + 1.0 x[1] + 1.0 x[2] + 1.0 x[3] + 1.0 x[4] + 1.0 x[5] + 1.0 x[6] + 1.0 x[7] + 1.0 x[8] + 1.0 x[9] + 1.0 x[10] + 1.0 x[11] + 1.0 x[12] + 1.0 x[13] + 1.0 x[14] + 1.0 x[15] + 1.0 x[16] + 1.0 x[17] + 1.0 x[18] + 1.0 x[19] + 1.0 x[20] + 1.0 x[21] + 1.0 x[22] + 1.0 x[23] + 1.0 x[24] + 1.0 x[25] + 1.0 x[26] + 1.0 x[27] + 1.0 x[28] + 1.0 x[29] + 1.0 x[30] + 1.0 x[31] + 1.0 x[32] + 1.0 x[33] + 1.0 x[34] + 1.0 x[35] + 1.0 x[36] + 1.0 x[37] + 1.0 x[38] + 1.0 x[39] + 1.0 x[40] + 1.0 x[41] + 1.0 x[42] + 1.0 x[43] + 1.0 x[44] + 1.0 x[45] + 1.0 x[46] + 1.0 x[47] + 1.0 x[48] + 1.0 x[49] + 1.0 x[50]│
└ ┘ ∈ Zeros(1)
VectorAffineFunction{Float64}-in-Nonnegatives
┌ ┐
│0.0 + 1.0 x[1]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[2]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[3]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[4]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[5]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[6]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[7]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[8]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[9]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[10]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[11]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[12]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[13]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[14]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[15]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[16]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[17]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[18]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[19]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[20]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[21]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[22]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[23]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[24]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[25]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[26]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[27]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[28]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[29]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[30]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[31]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[32]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[33]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[34]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[35]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[36]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[37]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[38]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[39]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[40]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[41]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[42]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[43]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[44]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[45]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[46]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[47]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[48]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[49]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[50]│
└ ┘ ∈ Nonnegatives(1)
Minimize ScalarQuadraticFunction{Float64}:
0.0 - 0.06771131628535806 x[1] - 0.09180012608728162 x[2] - 0.06375350814975125 x[3] - 0.07728697866070769 x[4] - 0.23074788730586093 x[5] - 0.15686249459348622 x[6] - 0.2122498655334816 x[7] - 0.20898817784579424 x[8] - 0.12227753843983823 x[9] - 0.12344088127344603 x[10] - 0.15545072902372237 x[11] - 0.16958105587116123 x[12] - 0.06834630988483259 x[13] - 0.2197260697430891 x[14] - 0.12988172171602164 x[15] - 0.13589973593997076 x[16] - 0.19320779480657374 x[17] - 0.23328900192334057 x[18] - 0.08051781121893438 x[19] - 0.14490751362815402 x[20] - 0.12547313972526974 x[21] - 0.1581396997706362 x[22] - 0.15439633611787326 x[23] - 0.12159506055577983 x[24] - 0.1837234858750337 x[25] - 0.10912305703834037 x[26] - 0.12706456147712303 x[27] - 0.22181496886937255 x[28] - 0.23852097577354414 x[29] - 0.20537835714828 x[30] - 0.1957487641599738 x[31] - 0.22325673774714186 x[32] - 0.19928112264427983 x[33] - 0.1629717834324734 x[34] - 0.06795427462774117 x[35] - 0.12678081212099138 x[36] - 0.15652700614197096 x[37] - 0.08450237789511361 x[38] - 0.12571123900337383 x[39] - 0.07866275342820206 x[40] - 0.192876825437647 x[41] - 0.10799914713371711 x[42] - 0.1520486948474937 x[43] - 0.08462491917729889 x[44] - 0.06772251627515226 x[45] - 0.23683810995974197 x[46] - 0.19633122919058085 x[47] - 0.1434881672660215 x[48] - 0.10107556274464907 x[49] - 0.12911042299961262 x[50] + 1.0 y[1]² + 1.0 y[2]² + 1.0 y[3]² + 1.0 y[4]² + 1.0 y[5]² + 0.22168311155166154 x[1]² + 1.569674359079319 x[2]² + 1.1253275636203313 x[3]² + 1.958440472561891 x[4]² + 2.1320134751461897 x[5]² + 1.1354989565743618 x[6]² + 1.7659372870351717 x[7]² + 0.1593290841959982 x[8]² + 0.3094227911776114 x[9]² + 0.8791977343224676 x[10]² + 0.39742223612651667 x[11]² + 1.8875918586267313 x[12]² + 1.8387120048986592 x[13]² + 2.190053109789465 x[14]² + 2.1957255604735644 x[15]² + 2.1978762529481384 x[16]² + 1.1710828933547 x[17]² + 1.2987007815595075 x[18]² + 0.281209441224692 x[19]² + 0.33479111624495367 x[20]² + 1.8966897412188368 x[21]² + 1.401948599916701 x[22]² + 2.160159812386103 x[23]² + 1.9353413223067184 x[24]² + 1.8453446813850807 x[25]² + 0.5624261051786525 x[26]² + 1.0198781850630045 x[27]² + 2.0113520898601918 x[28]² + 1.4681359454446885 x[29]² + 0.5963127696051644 x[30]² + 0.5175042820439373 x[31]² + 1.852649196595403 x[32]² + 1.8159596121340185 x[33]² + 0.6715708566047849 x[34]² + 0.546141819204228 x[35]² + 1.7261425935764683 x[36]² + 1.8841597069654406 x[37]² + 1.8282514435305761 x[38]² + 1.9568900128195392 x[39]² + 1.9503256911912632 x[40]² + 1.0526772112820373 x[41]² + 1.0229536502198167 x[42]² + 0.8792148153431698 x[43]² + 2.1254116542837194 x[44]² + 1.7521275518465191 x[45]² + 1.4534148949272803 x[46]² + 0.2944245797695367 x[47]² + 0.2754584682030851 x[48]² + 0.43199283796505494 x[49]² + 2.0761956200923155 x[50]²
Subject to:
VectorAffineFunction{Float64}-in-Zeros
┌ ┐
│0.0 - 0.45836571560595957 x[1] - 1.4882021641049918 x[2] + 2.1826127685114023 x[4] + 0.8239262467380715 x[6] - 1.2962721783934823 x[9] + 0.19983857542320999 x[11] - 1.435940970672912 x[13] + 1.194939742800976 x[18] - 0.7605416579955722 x[19] - 0.10198063634911336 x[20] + 0.0962615513861198 x[23] - 0.12018274708623239 x[26] - 0.7295613191446634 x[27] - 0.07270642655012116 x[28] - 0.8907108705599415 x[29] - 1.0051237161319388 x[30] - 0.8232754710476714 x[31] - 0.3127161299324051 x[32] - 0.7795842203334354 x[34] + 0.9216601059658592 x[35] - 2.069856046894368 x[36] - 0.5189602133669754 x[37] + 0.5885760717502199 x[38] - 0.7196314555287213 x[40] - 0.9291963494383236 x[43] - 0.17796544541790937 x[44] + 0.41792527291699105 x[45] + 0.5159420767895866 x[48] + 1.0 y[1]│
└ ┘ ∈ Zeros(1)
┌ ┐
│0.0 + 0.0503378286805425 x[4] + 1.1256748837213493 x[6] + 0.7658960317180369 x[8] - 0.061035008743322475 x[10] + 0.6046067312789892 x[11] + 1.683500023265881 x[12] + 1.201178638729371 x[13] + 0.6155732499801082 x[14] + 2.4402033735474125 x[23] - 0.7379012770819809 x[24] + 0.20489758707586392 x[25] + 1.2320869079191876 x[26] - 1.9402369852338388 x[27] - 0.954777195400799 x[31] - 0.344798870223836 x[32] + 0.17805576280533475 x[34] + 0.24224089365318544 x[37] - 1.7590069644534676 x[38] + 1.4165151237242104 x[40] + 0.8808123403489245 x[43] - 0.4474817348974519 x[44] + 0.8136739930455366 x[45] + 0.997384476726562 x[47] + 1.0 y[2]│
└ ┘ ∈ Zeros(1)
┌ ┐
│0.0 - 0.20209121321144838 x[1] + 1.157104812420386 x[2] + 0.45265959148235724 x[3] - 0.8009036795569376 x[4] - 2.0302615696038253 x[5] + 0.6241037854724422 x[6] + 0.8271047378482009 x[12] - 1.8249637555191254 x[14] + 0.054713116051507256 x[15] + 1.1115572615284857 x[17] + 1.7828304776409556 x[18] + 0.7423713791628864 x[19] + 0.5552255444433157 x[21] + 0.2303118558750502 x[22] + 0.10973142914455558 x[23] - 0.16181023670093883 x[25] + 1.7265600749058716 x[26] + 1.0154508128378734 x[30] - 0.9272881543745629 x[32] - 0.8528545030926377 x[34] - 0.8887796114735067 x[35] - 0.6372939953316094 x[37] - 2.0729975098289883 x[38] + 0.21793972328895084 x[39] + 0.5968016554494258 x[40] + 0.8446725934201121 x[41] - 0.6564960898033011 x[42] - 0.2577617922174006 x[45] + 1.6066125045474893 x[47] - 0.6106753315638065 x[49] - 0.24094934017892947 x[50] + 1.0 y[3]│
└ ┘ ∈ Zeros(1)
┌ ┐
│0.0 + 0.24314199505818793 x[2] - 1.3876541437893315 x[4] - 0.22683790735634463 x[6] + 0.5214802680235079 x[7] + 1.3354590673591633 x[8] - 1.8504774775149704 x[9] + 0.23051379143328576 x[13] - 0.1572785018821299 x[14] - 1.483039278741509 x[15] - 0.26226284250578463 x[16] - 0.0986696994672989 x[17] - 0.08550126212770054 x[20] + 0.3419778094275683 x[22] + 0.06543821802916351 x[23] - 0.2207564607343709 x[25] - 0.6273452593617963 x[26] + 0.37311820250796757 x[27] - 1.1054210865179164 x[28] + 0.5615671906319677 x[29] - 0.1030742062121358 x[30] - 0.13774215623815417 x[31] + 0.4839037548487663 x[33] + 0.8926885669157067 x[34] - 2.5405468288052515 x[35] + 0.2874685755965493 x[36] - 0.23047583769083854 x[39] + 1.1096979208454745 x[40] + 1.3964654491745603 x[44] - 0.5374828725846994 x[45] + 1.4520935910396786 x[47] + 1.0 y[4]│
└ ┘ ∈ Zeros(1)
┌ ┐
│0.0 - 1.4139342679089253 x[1] - 0.35072192922287954 x[5] + 1.652168425225477 x[7] - 0.049113526881893764 x[18] - 0.8682023381498042 x[22] - 1.5204662064824461 x[23] - 1.3700941514175726 x[24] + 0.05398461169426838 x[25] + 0.013219813753395412 x[26] - 0.8595562201704314 x[31] + 2.3073642877859806 x[33] + 0.0566217713770541 x[35] + 0.12661760952546483 x[40] + 1.4067743147522846 x[41] - 1.2155494239575593 x[43] - 0.24750058660020918 x[47] - 1.7920247650821086 x[49] + 1.0 y[5]│
└ ┘ ∈ Zeros(1)
┌ ┐
│-1.0 + 1.0 x[1] + 1.0 x[2] + 1.0 x[3] + 1.0 x[4] + 1.0 x[5] + 1.0 x[6] + 1.0 x[7] + 1.0 x[8] + 1.0 x[9] + 1.0 x[10] + 1.0 x[11] + 1.0 x[12] + 1.0 x[13] + 1.0 x[14] + 1.0 x[15] + 1.0 x[16] + 1.0 x[17] + 1.0 x[18] + 1.0 x[19] + 1.0 x[20] + 1.0 x[21] + 1.0 x[22] + 1.0 x[23] + 1.0 x[24] + 1.0 x[25] + 1.0 x[26] + 1.0 x[27] + 1.0 x[28] + 1.0 x[29] + 1.0 x[30] + 1.0 x[31] + 1.0 x[32] + 1.0 x[33] + 1.0 x[34] + 1.0 x[35] + 1.0 x[36] + 1.0 x[37] + 1.0 x[38] + 1.0 x[39] + 1.0 x[40] + 1.0 x[41] + 1.0 x[42] + 1.0 x[43] + 1.0 x[44] + 1.0 x[45] + 1.0 x[46] + 1.0 x[47] + 1.0 x[48] + 1.0 x[49] + 1.0 x[50]│
└ ┘ ∈ Zeros(1)
VectorAffineFunction{Float64}-in-Nonnegatives
┌ ┐
│0.0 + 1.0 x[1]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[2]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[3]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[4]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[5]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[6]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[7]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[8]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[9]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[10]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[11]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[12]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[13]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[14]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[15]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[16]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[17]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[18]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[19]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[20]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[21]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[22]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[23]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[24]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[25]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[26]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[27]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[28]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[29]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[30]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[31]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[32]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[33]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[34]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[35]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[36]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[37]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[38]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[39]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[40]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[41]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[42]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[43]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[44]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[45]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[46]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[47]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[48]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[49]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[50]│
└ ┘ ∈ Nonnegatives(1)
Minimize ScalarQuadraticFunction{Float64}:
0.0 - 0.03385565814267903 x[1] - 0.04590006304364081 x[2] - 0.03187675407487563 x[3] - 0.038643489330353845 x[4] - 0.11537394365293047 x[5] - 0.07843124729674311 x[6] - 0.1061249327667408 x[7] - 0.10449408892289712 x[8] - 0.06113876921991911 x[9] - 0.061720440636723016 x[10] - 0.07772536451186118 x[11] - 0.08479052793558062 x[12] - 0.034173154942416295 x[13] - 0.10986303487154454 x[14] - 0.06494086085801082 x[15] - 0.06794986796998538 x[16] - 0.09660389740328687 x[17] - 0.11664450096167028 x[18] - 0.04025890560946719 x[19] - 0.07245375681407701 x[20] - 0.06273656986263487 x[21] - 0.0790698498853181 x[22] - 0.07719816805893663 x[23] - 0.060797530277889915 x[24] - 0.09186174293751685 x[25] - 0.054561528519170184 x[26] - 0.06353228073856151 x[27] - 0.11090748443468627 x[28] - 0.11926048788677207 x[29] - 0.10268917857414 x[30] - 0.0978743820799869 x[31] - 0.11162836887357093 x[32] - 0.09964056132213991 x[33] - 0.0814858917162367 x[34] - 0.03397713731387059 x[35] - 0.06339040606049569 x[36] - 0.07826350307098548 x[37] - 0.042251188947556806 x[38] - 0.06285561950168692 x[39] - 0.03933137671410103 x[40] - 0.0964384127188235 x[41] - 0.053999573566858555 x[42] - 0.07602434742374685 x[43] - 0.042312459588649445 x[44] - 0.03386125813757613 x[45] - 0.11841905497987099 x[46] - 0.09816561459529043 x[47] - 0.07174408363301076 x[48] - 0.050537781372324536 x[49] - 0.06455521149980631 x[50] + 1.0 y[1]² + 1.0 y[2]² + 1.0 y[3]² + 1.0 y[4]² + 1.0 y[5]² + 0.22168311155166154 x[1]² + 1.569674359079319 x[2]² + 1.1253275636203313 x[3]² + 1.958440472561891 x[4]² + 2.1320134751461897 x[5]² + 1.1354989565743618 x[6]² + 1.7659372870351717 x[7]² + 0.1593290841959982 x[8]² + 0.3094227911776114 x[9]² + 0.8791977343224676 x[10]² + 0.39742223612651667 x[11]² + 1.8875918586267313 x[12]² + 1.8387120048986592 x[13]² + 2.190053109789465 x[14]² + 2.1957255604735644 x[15]² + 2.1978762529481384 x[16]² + 1.1710828933547 x[17]² + 1.2987007815595075 x[18]² + 0.281209441224692 x[19]² + 0.33479111624495367 x[20]² + 1.8966897412188368 x[21]² + 1.401948599916701 x[22]² + 2.160159812386103 x[23]² + 1.9353413223067184 x[24]² + 1.8453446813850807 x[25]² + 0.5624261051786525 x[26]² + 1.0198781850630045 x[27]² + 2.0113520898601918 x[28]² + 1.4681359454446885 x[29]² + 0.5963127696051644 x[30]² + 0.5175042820439373 x[31]² + 1.852649196595403 x[32]² + 1.8159596121340185 x[33]² + 0.6715708566047849 x[34]² + 0.546141819204228 x[35]² + 1.7261425935764683 x[36]² + 1.8841597069654406 x[37]² + 1.8282514435305761 x[38]² + 1.9568900128195392 x[39]² + 1.9503256911912632 x[40]² + 1.0526772112820373 x[41]² + 1.0229536502198167 x[42]² + 0.8792148153431698 x[43]² + 2.1254116542837194 x[44]² + 1.7521275518465191 x[45]² + 1.4534148949272803 x[46]² + 0.2944245797695367 x[47]² + 0.2754584682030851 x[48]² + 0.43199283796505494 x[49]² + 2.0761956200923155 x[50]²
Subject to:
VectorAffineFunction{Float64}-in-Zeros
┌ ┐
│0.0 - 0.45836571560595957 x[1] - 1.4882021641049918 x[2] + 2.1826127685114023 x[4] + 0.8239262467380715 x[6] - 1.2962721783934823 x[9] + 0.19983857542320999 x[11] - 1.435940970672912 x[13] + 1.194939742800976 x[18] - 0.7605416579955722 x[19] - 0.10198063634911336 x[20] + 0.0962615513861198 x[23] - 0.12018274708623239 x[26] - 0.7295613191446634 x[27] - 0.07270642655012116 x[28] - 0.8907108705599415 x[29] - 1.0051237161319388 x[30] - 0.8232754710476714 x[31] - 0.3127161299324051 x[32] - 0.7795842203334354 x[34] + 0.9216601059658592 x[35] - 2.069856046894368 x[36] - 0.5189602133669754 x[37] + 0.5885760717502199 x[38] - 0.7196314555287213 x[40] - 0.9291963494383236 x[43] - 0.17796544541790937 x[44] + 0.41792527291699105 x[45] + 0.5159420767895866 x[48] + 1.0 y[1]│
└ ┘ ∈ Zeros(1)
┌ ┐
│0.0 + 0.0503378286805425 x[4] + 1.1256748837213493 x[6] + 0.7658960317180369 x[8] - 0.061035008743322475 x[10] + 0.6046067312789892 x[11] + 1.683500023265881 x[12] + 1.201178638729371 x[13] + 0.6155732499801082 x[14] + 2.4402033735474125 x[23] - 0.7379012770819809 x[24] + 0.20489758707586392 x[25] + 1.2320869079191876 x[26] - 1.9402369852338388 x[27] - 0.954777195400799 x[31] - 0.344798870223836 x[32] + 0.17805576280533475 x[34] + 0.24224089365318544 x[37] - 1.7590069644534676 x[38] + 1.4165151237242104 x[40] + 0.8808123403489245 x[43] - 0.4474817348974519 x[44] + 0.8136739930455366 x[45] + 0.997384476726562 x[47] + 1.0 y[2]│
└ ┘ ∈ Zeros(1)
┌ ┐
│0.0 - 0.20209121321144838 x[1] + 1.157104812420386 x[2] + 0.45265959148235724 x[3] - 0.8009036795569376 x[4] - 2.0302615696038253 x[5] + 0.6241037854724422 x[6] + 0.8271047378482009 x[12] - 1.8249637555191254 x[14] + 0.054713116051507256 x[15] + 1.1115572615284857 x[17] + 1.7828304776409556 x[18] + 0.7423713791628864 x[19] + 0.5552255444433157 x[21] + 0.2303118558750502 x[22] + 0.10973142914455558 x[23] - 0.16181023670093883 x[25] + 1.7265600749058716 x[26] + 1.0154508128378734 x[30] - 0.9272881543745629 x[32] - 0.8528545030926377 x[34] - 0.8887796114735067 x[35] - 0.6372939953316094 x[37] - 2.0729975098289883 x[38] + 0.21793972328895084 x[39] + 0.5968016554494258 x[40] + 0.8446725934201121 x[41] - 0.6564960898033011 x[42] - 0.2577617922174006 x[45] + 1.6066125045474893 x[47] - 0.6106753315638065 x[49] - 0.24094934017892947 x[50] + 1.0 y[3]│
└ ┘ ∈ Zeros(1)
┌ ┐
│0.0 + 0.24314199505818793 x[2] - 1.3876541437893315 x[4] - 0.22683790735634463 x[6] + 0.5214802680235079 x[7] + 1.3354590673591633 x[8] - 1.8504774775149704 x[9] + 0.23051379143328576 x[13] - 0.1572785018821299 x[14] - 1.483039278741509 x[15] - 0.26226284250578463 x[16] - 0.0986696994672989 x[17] - 0.08550126212770054 x[20] + 0.3419778094275683 x[22] + 0.06543821802916351 x[23] - 0.2207564607343709 x[25] - 0.6273452593617963 x[26] + 0.37311820250796757 x[27] - 1.1054210865179164 x[28] + 0.5615671906319677 x[29] - 0.1030742062121358 x[30] - 0.13774215623815417 x[31] + 0.4839037548487663 x[33] + 0.8926885669157067 x[34] - 2.5405468288052515 x[35] + 0.2874685755965493 x[36] - 0.23047583769083854 x[39] + 1.1096979208454745 x[40] + 1.3964654491745603 x[44] - 0.5374828725846994 x[45] + 1.4520935910396786 x[47] + 1.0 y[4]│
└ ┘ ∈ Zeros(1)
┌ ┐
│0.0 - 1.4139342679089253 x[1] - 0.35072192922287954 x[5] + 1.652168425225477 x[7] - 0.049113526881893764 x[18] - 0.8682023381498042 x[22] - 1.5204662064824461 x[23] - 1.3700941514175726 x[24] + 0.05398461169426838 x[25] + 0.013219813753395412 x[26] - 0.8595562201704314 x[31] + 2.3073642877859806 x[33] + 0.0566217713770541 x[35] + 0.12661760952546483 x[40] + 1.4067743147522846 x[41] - 1.2155494239575593 x[43] - 0.24750058660020918 x[47] - 1.7920247650821086 x[49] + 1.0 y[5]│
└ ┘ ∈ Zeros(1)
┌ ┐
│-1.0 + 1.0 x[1] + 1.0 x[2] + 1.0 x[3] + 1.0 x[4] + 1.0 x[5] + 1.0 x[6] + 1.0 x[7] + 1.0 x[8] + 1.0 x[9] + 1.0 x[10] + 1.0 x[11] + 1.0 x[12] + 1.0 x[13] + 1.0 x[14] + 1.0 x[15] + 1.0 x[16] + 1.0 x[17] + 1.0 x[18] + 1.0 x[19] + 1.0 x[20] + 1.0 x[21] + 1.0 x[22] + 1.0 x[23] + 1.0 x[24] + 1.0 x[25] + 1.0 x[26] + 1.0 x[27] + 1.0 x[28] + 1.0 x[29] + 1.0 x[30] + 1.0 x[31] + 1.0 x[32] + 1.0 x[33] + 1.0 x[34] + 1.0 x[35] + 1.0 x[36] + 1.0 x[37] + 1.0 x[38] + 1.0 x[39] + 1.0 x[40] + 1.0 x[41] + 1.0 x[42] + 1.0 x[43] + 1.0 x[44] + 1.0 x[45] + 1.0 x[46] + 1.0 x[47] + 1.0 x[48] + 1.0 x[49] + 1.0 x[50]│
└ ┘ ∈ Zeros(1)
VectorAffineFunction{Float64}-in-Nonnegatives
┌ ┐
│0.0 + 1.0 x[1]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[2]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[3]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[4]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[5]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[6]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[7]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[8]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[9]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[10]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[11]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[12]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[13]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[14]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[15]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[16]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[17]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[18]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[19]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[20]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[21]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[22]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[23]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[24]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[25]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[26]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[27]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[28]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[29]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[30]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[31]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[32]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[33]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[34]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[35]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[36]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[37]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[38]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[39]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[40]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[41]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[42]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[43]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[44]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[45]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[46]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[47]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[48]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[49]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[50]│
└ ┘ ∈ Nonnegatives(1)
Minimize ScalarQuadraticFunction{Float64}:
0.0 - 0.01128521938089301 x[1] - 0.015300021014546937 x[2] - 0.010625584691625209 x[3] - 0.012881163110117947 x[4] - 0.03845798121764349 x[5] - 0.02614374909891437 x[6] - 0.0353749775889136 x[7] - 0.034831362974299035 x[8] - 0.020379589739973038 x[9] - 0.020573480212241004 x[10] - 0.02590845483728706 x[11] - 0.028263509311860203 x[12] - 0.011391051647472098 x[13] - 0.036621011623848176 x[14] - 0.02164695361933694 x[15] - 0.022649955989995127 x[16] - 0.03220129913442896 x[17] - 0.03888150032055676 x[18] - 0.01341963520315573 x[19] - 0.024151252271359003 x[20] - 0.020912189954211624 x[21] - 0.026356616628439362 x[22] - 0.025732722686312208 x[23] - 0.020265843425963305 x[24] - 0.030620580979172283 x[25] - 0.018187176173056728 x[26] - 0.021177426912853837 x[27] - 0.036969161478228756 x[28] - 0.03975349596225736 x[29] - 0.03422972619138 x[30] - 0.032624794026662296 x[31] - 0.03720945629119031 x[32] - 0.0332135204407133 x[33] - 0.027161963905412232 x[34] - 0.011325712437956862 x[35] - 0.02113013535349856 x[36] - 0.02608783435699516 x[37] - 0.0140837296491856 x[38] - 0.02095187316722897 x[39] - 0.013110458904700343 x[40] - 0.032146137572941165 x[41] - 0.017999857855619517 x[42] - 0.02534144914124895 x[43] - 0.014104153196216482 x[44] - 0.01128708604585871 x[45] - 0.03947301832662366 x[46] - 0.03272187153176347 x[47] - 0.023914694544336916 x[48] - 0.01684592712410818 x[49] - 0.02151840383326877 x[50] + 1.0 y[1]² + 1.0 y[2]² + 1.0 y[3]² + 1.0 y[4]² + 1.0 y[5]² + 0.22168311155166154 x[1]² + 1.569674359079319 x[2]² + 1.1253275636203313 x[3]² + 1.958440472561891 x[4]² + 2.1320134751461897 x[5]² + 1.1354989565743618 x[6]² + 1.7659372870351717 x[7]² + 0.1593290841959982 x[8]² + 0.3094227911776114 x[9]² + 0.8791977343224676 x[10]² + 0.39742223612651667 x[11]² + 1.8875918586267313 x[12]² + 1.8387120048986592 x[13]² + 2.190053109789465 x[14]² + 2.1957255604735644 x[15]² + 2.1978762529481384 x[16]² + 1.1710828933547 x[17]² + 1.2987007815595075 x[18]² + 0.281209441224692 x[19]² + 0.33479111624495367 x[20]² + 1.8966897412188368 x[21]² + 1.401948599916701 x[22]² + 2.160159812386103 x[23]² + 1.9353413223067184 x[24]² + 1.8453446813850807 x[25]² + 0.5624261051786525 x[26]² + 1.0198781850630045 x[27]² + 2.0113520898601918 x[28]² + 1.4681359454446885 x[29]² + 0.5963127696051644 x[30]² + 0.5175042820439373 x[31]² + 1.852649196595403 x[32]² + 1.8159596121340185 x[33]² + 0.6715708566047849 x[34]² + 0.546141819204228 x[35]² + 1.7261425935764683 x[36]² + 1.8841597069654406 x[37]² + 1.8282514435305761 x[38]² + 1.9568900128195392 x[39]² + 1.9503256911912632 x[40]² + 1.0526772112820373 x[41]² + 1.0229536502198167 x[42]² + 0.8792148153431698 x[43]² + 2.1254116542837194 x[44]² + 1.7521275518465191 x[45]² + 1.4534148949272803 x[46]² + 0.2944245797695367 x[47]² + 0.2754584682030851 x[48]² + 0.43199283796505494 x[49]² + 2.0761956200923155 x[50]²
Subject to:
VectorAffineFunction{Float64}-in-Zeros
┌ ┐
│0.0 - 0.45836571560595957 x[1] - 1.4882021641049918 x[2] + 2.1826127685114023 x[4] + 0.8239262467380715 x[6] - 1.2962721783934823 x[9] + 0.19983857542320999 x[11] - 1.435940970672912 x[13] + 1.194939742800976 x[18] - 0.7605416579955722 x[19] - 0.10198063634911336 x[20] + 0.0962615513861198 x[23] - 0.12018274708623239 x[26] - 0.7295613191446634 x[27] - 0.07270642655012116 x[28] - 0.8907108705599415 x[29] - 1.0051237161319388 x[30] - 0.8232754710476714 x[31] - 0.3127161299324051 x[32] - 0.7795842203334354 x[34] + 0.9216601059658592 x[35] - 2.069856046894368 x[36] - 0.5189602133669754 x[37] + 0.5885760717502199 x[38] - 0.7196314555287213 x[40] - 0.9291963494383236 x[43] - 0.17796544541790937 x[44] + 0.41792527291699105 x[45] + 0.5159420767895866 x[48] + 1.0 y[1]│
└ ┘ ∈ Zeros(1)
┌ ┐
│0.0 + 0.0503378286805425 x[4] + 1.1256748837213493 x[6] + 0.7658960317180369 x[8] - 0.061035008743322475 x[10] + 0.6046067312789892 x[11] + 1.683500023265881 x[12] + 1.201178638729371 x[13] + 0.6155732499801082 x[14] + 2.4402033735474125 x[23] - 0.7379012770819809 x[24] + 0.20489758707586392 x[25] + 1.2320869079191876 x[26] - 1.9402369852338388 x[27] - 0.954777195400799 x[31] - 0.344798870223836 x[32] + 0.17805576280533475 x[34] + 0.24224089365318544 x[37] - 1.7590069644534676 x[38] + 1.4165151237242104 x[40] + 0.8808123403489245 x[43] - 0.4474817348974519 x[44] + 0.8136739930455366 x[45] + 0.997384476726562 x[47] + 1.0 y[2]│
└ ┘ ∈ Zeros(1)
┌ ┐
│0.0 - 0.20209121321144838 x[1] + 1.157104812420386 x[2] + 0.45265959148235724 x[3] - 0.8009036795569376 x[4] - 2.0302615696038253 x[5] + 0.6241037854724422 x[6] + 0.8271047378482009 x[12] - 1.8249637555191254 x[14] + 0.054713116051507256 x[15] + 1.1115572615284857 x[17] + 1.7828304776409556 x[18] + 0.7423713791628864 x[19] + 0.5552255444433157 x[21] + 0.2303118558750502 x[22] + 0.10973142914455558 x[23] - 0.16181023670093883 x[25] + 1.7265600749058716 x[26] + 1.0154508128378734 x[30] - 0.9272881543745629 x[32] - 0.8528545030926377 x[34] - 0.8887796114735067 x[35] - 0.6372939953316094 x[37] - 2.0729975098289883 x[38] + 0.21793972328895084 x[39] + 0.5968016554494258 x[40] + 0.8446725934201121 x[41] - 0.6564960898033011 x[42] - 0.2577617922174006 x[45] + 1.6066125045474893 x[47] - 0.6106753315638065 x[49] - 0.24094934017892947 x[50] + 1.0 y[3]│
└ ┘ ∈ Zeros(1)
┌ ┐
│0.0 + 0.24314199505818793 x[2] - 1.3876541437893315 x[4] - 0.22683790735634463 x[6] + 0.5214802680235079 x[7] + 1.3354590673591633 x[8] - 1.8504774775149704 x[9] + 0.23051379143328576 x[13] - 0.1572785018821299 x[14] - 1.483039278741509 x[15] - 0.26226284250578463 x[16] - 0.0986696994672989 x[17] - 0.08550126212770054 x[20] + 0.3419778094275683 x[22] + 0.06543821802916351 x[23] - 0.2207564607343709 x[25] - 0.6273452593617963 x[26] + 0.37311820250796757 x[27] - 1.1054210865179164 x[28] + 0.5615671906319677 x[29] - 0.1030742062121358 x[30] - 0.13774215623815417 x[31] + 0.4839037548487663 x[33] + 0.8926885669157067 x[34] - 2.5405468288052515 x[35] + 0.2874685755965493 x[36] - 0.23047583769083854 x[39] + 1.1096979208454745 x[40] + 1.3964654491745603 x[44] - 0.5374828725846994 x[45] + 1.4520935910396786 x[47] + 1.0 y[4]│
└ ┘ ∈ Zeros(1)
┌ ┐
│0.0 - 1.4139342679089253 x[1] - 0.35072192922287954 x[5] + 1.652168425225477 x[7] - 0.049113526881893764 x[18] - 0.8682023381498042 x[22] - 1.5204662064824461 x[23] - 1.3700941514175726 x[24] + 0.05398461169426838 x[25] + 0.013219813753395412 x[26] - 0.8595562201704314 x[31] + 2.3073642877859806 x[33] + 0.0566217713770541 x[35] + 0.12661760952546483 x[40] + 1.4067743147522846 x[41] - 1.2155494239575593 x[43] - 0.24750058660020918 x[47] - 1.7920247650821086 x[49] + 1.0 y[5]│
└ ┘ ∈ Zeros(1)
┌ ┐
│-1.0 + 1.0 x[1] + 1.0 x[2] + 1.0 x[3] + 1.0 x[4] + 1.0 x[5] + 1.0 x[6] + 1.0 x[7] + 1.0 x[8] + 1.0 x[9] + 1.0 x[10] + 1.0 x[11] + 1.0 x[12] + 1.0 x[13] + 1.0 x[14] + 1.0 x[15] + 1.0 x[16] + 1.0 x[17] + 1.0 x[18] + 1.0 x[19] + 1.0 x[20] + 1.0 x[21] + 1.0 x[22] + 1.0 x[23] + 1.0 x[24] + 1.0 x[25] + 1.0 x[26] + 1.0 x[27] + 1.0 x[28] + 1.0 x[29] + 1.0 x[30] + 1.0 x[31] + 1.0 x[32] + 1.0 x[33] + 1.0 x[34] + 1.0 x[35] + 1.0 x[36] + 1.0 x[37] + 1.0 x[38] + 1.0 x[39] + 1.0 x[40] + 1.0 x[41] + 1.0 x[42] + 1.0 x[43] + 1.0 x[44] + 1.0 x[45] + 1.0 x[46] + 1.0 x[47] + 1.0 x[48] + 1.0 x[49] + 1.0 x[50]│
└ ┘ ∈ Zeros(1)
VectorAffineFunction{Float64}-in-Nonnegatives
┌ ┐
│0.0 + 1.0 x[1]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[2]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[3]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[4]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[5]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[6]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[7]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[8]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[9]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[10]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[11]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[12]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[13]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[14]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[15]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[16]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[17]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[18]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[19]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[20]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[21]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[22]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[23]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[24]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[25]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[26]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[27]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[28]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[29]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[30]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[31]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[32]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[33]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[34]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[35]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[36]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[37]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[38]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[39]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[40]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[41]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[42]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[43]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[44]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[45]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[46]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[47]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[48]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[49]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[50]│
└ ┘ ∈ Nonnegatives(1)
Minimize ScalarQuadraticFunction{Float64}:
0.0 - 0.003385565814267903 x[1] - 0.0045900063043640815 x[2] - 0.003187675407487563 x[3] - 0.0038643489330353847 x[4] - 0.011537394365293047 x[5] - 0.007843124729674312 x[6] - 0.01061249327667408 x[7] - 0.010449408892289713 x[8] - 0.0061138769219919115 x[9] - 0.006172044063672302 x[10] - 0.007772536451186119 x[11] - 0.008479052793558062 x[12] - 0.0034173154942416296 x[13] - 0.010986303487154455 x[14] - 0.006494086085801082 x[15] - 0.006794986796998539 x[16] - 0.009660389740328687 x[17] - 0.011664450096167029 x[18] - 0.0040258905609467195 x[19] - 0.007245375681407701 x[20] - 0.006273656986263487 x[21] - 0.007906984988531809 x[22] - 0.0077198168058936634 x[23] - 0.006079753027788992 x[24] - 0.009186174293751686 x[25] - 0.005456152851917018 x[26] - 0.006353228073856152 x[27] - 0.011090748443468627 x[28] - 0.011926048788677208 x[29] - 0.010268917857414002 x[30] - 0.00978743820799869 x[31] - 0.011162836887357093 x[32] - 0.009964056132213992 x[33] - 0.00814858917162367 x[34] - 0.0033977137313870587 x[35] - 0.006339040606049569 x[36] - 0.007826350307098549 x[37] - 0.004225118894755681 x[38] - 0.006285561950168692 x[39] - 0.0039331376714101035 x[40] - 0.00964384127188235 x[41] - 0.005399957356685856 x[42] - 0.007602434742374685 x[43] - 0.004231245958864945 x[44] - 0.003386125813757613 x[45] - 0.0118419054979871 x[46] - 0.009816561459529043 x[47] - 0.007174408363301076 x[48] - 0.005053778137232454 x[49] - 0.006455521149980631 x[50] + 1.0 y[1]² + 1.0 y[2]² + 1.0 y[3]² + 1.0 y[4]² + 1.0 y[5]² + 0.22168311155166154 x[1]² + 1.569674359079319 x[2]² + 1.1253275636203313 x[3]² + 1.958440472561891 x[4]² + 2.1320134751461897 x[5]² + 1.1354989565743618 x[6]² + 1.7659372870351717 x[7]² + 0.1593290841959982 x[8]² + 0.3094227911776114 x[9]² + 0.8791977343224676 x[10]² + 0.39742223612651667 x[11]² + 1.8875918586267313 x[12]² + 1.8387120048986592 x[13]² + 2.190053109789465 x[14]² + 2.1957255604735644 x[15]² + 2.1978762529481384 x[16]² + 1.1710828933547 x[17]² + 1.2987007815595075 x[18]² + 0.281209441224692 x[19]² + 0.33479111624495367 x[20]² + 1.8966897412188368 x[21]² + 1.401948599916701 x[22]² + 2.160159812386103 x[23]² + 1.9353413223067184 x[24]² + 1.8453446813850807 x[25]² + 0.5624261051786525 x[26]² + 1.0198781850630045 x[27]² + 2.0113520898601918 x[28]² + 1.4681359454446885 x[29]² + 0.5963127696051644 x[30]² + 0.5175042820439373 x[31]² + 1.852649196595403 x[32]² + 1.8159596121340185 x[33]² + 0.6715708566047849 x[34]² + 0.546141819204228 x[35]² + 1.7261425935764683 x[36]² + 1.8841597069654406 x[37]² + 1.8282514435305761 x[38]² + 1.9568900128195392 x[39]² + 1.9503256911912632 x[40]² + 1.0526772112820373 x[41]² + 1.0229536502198167 x[42]² + 0.8792148153431698 x[43]² + 2.1254116542837194 x[44]² + 1.7521275518465191 x[45]² + 1.4534148949272803 x[46]² + 0.2944245797695367 x[47]² + 0.2754584682030851 x[48]² + 0.43199283796505494 x[49]² + 2.0761956200923155 x[50]²
Subject to:
VectorAffineFunction{Float64}-in-Zeros
┌ ┐
│0.0 - 0.45836571560595957 x[1] - 1.4882021641049918 x[2] + 2.1826127685114023 x[4] + 0.8239262467380715 x[6] - 1.2962721783934823 x[9] + 0.19983857542320999 x[11] - 1.435940970672912 x[13] + 1.194939742800976 x[18] - 0.7605416579955722 x[19] - 0.10198063634911336 x[20] + 0.0962615513861198 x[23] - 0.12018274708623239 x[26] - 0.7295613191446634 x[27] - 0.07270642655012116 x[28] - 0.8907108705599415 x[29] - 1.0051237161319388 x[30] - 0.8232754710476714 x[31] - 0.3127161299324051 x[32] - 0.7795842203334354 x[34] + 0.9216601059658592 x[35] - 2.069856046894368 x[36] - 0.5189602133669754 x[37] + 0.5885760717502199 x[38] - 0.7196314555287213 x[40] - 0.9291963494383236 x[43] - 0.17796544541790937 x[44] + 0.41792527291699105 x[45] + 0.5159420767895866 x[48] + 1.0 y[1]│
└ ┘ ∈ Zeros(1)
┌ ┐
│0.0 + 0.0503378286805425 x[4] + 1.1256748837213493 x[6] + 0.7658960317180369 x[8] - 0.061035008743322475 x[10] + 0.6046067312789892 x[11] + 1.683500023265881 x[12] + 1.201178638729371 x[13] + 0.6155732499801082 x[14] + 2.4402033735474125 x[23] - 0.7379012770819809 x[24] + 0.20489758707586392 x[25] + 1.2320869079191876 x[26] - 1.9402369852338388 x[27] - 0.954777195400799 x[31] - 0.344798870223836 x[32] + 0.17805576280533475 x[34] + 0.24224089365318544 x[37] - 1.7590069644534676 x[38] + 1.4165151237242104 x[40] + 0.8808123403489245 x[43] - 0.4474817348974519 x[44] + 0.8136739930455366 x[45] + 0.997384476726562 x[47] + 1.0 y[2]│
└ ┘ ∈ Zeros(1)
┌ ┐
│0.0 - 0.20209121321144838 x[1] + 1.157104812420386 x[2] + 0.45265959148235724 x[3] - 0.8009036795569376 x[4] - 2.0302615696038253 x[5] + 0.6241037854724422 x[6] + 0.8271047378482009 x[12] - 1.8249637555191254 x[14] + 0.054713116051507256 x[15] + 1.1115572615284857 x[17] + 1.7828304776409556 x[18] + 0.7423713791628864 x[19] + 0.5552255444433157 x[21] + 0.2303118558750502 x[22] + 0.10973142914455558 x[23] - 0.16181023670093883 x[25] + 1.7265600749058716 x[26] + 1.0154508128378734 x[30] - 0.9272881543745629 x[32] - 0.8528545030926377 x[34] - 0.8887796114735067 x[35] - 0.6372939953316094 x[37] - 2.0729975098289883 x[38] + 0.21793972328895084 x[39] + 0.5968016554494258 x[40] + 0.8446725934201121 x[41] - 0.6564960898033011 x[42] - 0.2577617922174006 x[45] + 1.6066125045474893 x[47] - 0.6106753315638065 x[49] - 0.24094934017892947 x[50] + 1.0 y[3]│
└ ┘ ∈ Zeros(1)
┌ ┐
│0.0 + 0.24314199505818793 x[2] - 1.3876541437893315 x[4] - 0.22683790735634463 x[6] + 0.5214802680235079 x[7] + 1.3354590673591633 x[8] - 1.8504774775149704 x[9] + 0.23051379143328576 x[13] - 0.1572785018821299 x[14] - 1.483039278741509 x[15] - 0.26226284250578463 x[16] - 0.0986696994672989 x[17] - 0.08550126212770054 x[20] + 0.3419778094275683 x[22] + 0.06543821802916351 x[23] - 0.2207564607343709 x[25] - 0.6273452593617963 x[26] + 0.37311820250796757 x[27] - 1.1054210865179164 x[28] + 0.5615671906319677 x[29] - 0.1030742062121358 x[30] - 0.13774215623815417 x[31] + 0.4839037548487663 x[33] + 0.8926885669157067 x[34] - 2.5405468288052515 x[35] + 0.2874685755965493 x[36] - 0.23047583769083854 x[39] + 1.1096979208454745 x[40] + 1.3964654491745603 x[44] - 0.5374828725846994 x[45] + 1.4520935910396786 x[47] + 1.0 y[4]│
└ ┘ ∈ Zeros(1)
┌ ┐
│0.0 - 1.4139342679089253 x[1] - 0.35072192922287954 x[5] + 1.652168425225477 x[7] - 0.049113526881893764 x[18] - 0.8682023381498042 x[22] - 1.5204662064824461 x[23] - 1.3700941514175726 x[24] + 0.05398461169426838 x[25] + 0.013219813753395412 x[26] - 0.8595562201704314 x[31] + 2.3073642877859806 x[33] + 0.0566217713770541 x[35] + 0.12661760952546483 x[40] + 1.4067743147522846 x[41] - 1.2155494239575593 x[43] - 0.24750058660020918 x[47] - 1.7920247650821086 x[49] + 1.0 y[5]│
└ ┘ ∈ Zeros(1)
┌ ┐
│-1.0 + 1.0 x[1] + 1.0 x[2] + 1.0 x[3] + 1.0 x[4] + 1.0 x[5] + 1.0 x[6] + 1.0 x[7] + 1.0 x[8] + 1.0 x[9] + 1.0 x[10] + 1.0 x[11] + 1.0 x[12] + 1.0 x[13] + 1.0 x[14] + 1.0 x[15] + 1.0 x[16] + 1.0 x[17] + 1.0 x[18] + 1.0 x[19] + 1.0 x[20] + 1.0 x[21] + 1.0 x[22] + 1.0 x[23] + 1.0 x[24] + 1.0 x[25] + 1.0 x[26] + 1.0 x[27] + 1.0 x[28] + 1.0 x[29] + 1.0 x[30] + 1.0 x[31] + 1.0 x[32] + 1.0 x[33] + 1.0 x[34] + 1.0 x[35] + 1.0 x[36] + 1.0 x[37] + 1.0 x[38] + 1.0 x[39] + 1.0 x[40] + 1.0 x[41] + 1.0 x[42] + 1.0 x[43] + 1.0 x[44] + 1.0 x[45] + 1.0 x[46] + 1.0 x[47] + 1.0 x[48] + 1.0 x[49] + 1.0 x[50]│
└ ┘ ∈ Zeros(1)
VectorAffineFunction{Float64}-in-Nonnegatives
┌ ┐
│0.0 + 1.0 x[1]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[2]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[3]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[4]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[5]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[6]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[7]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[8]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[9]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[10]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[11]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[12]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[13]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[14]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[15]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[16]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[17]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[18]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[19]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[20]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[21]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[22]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[23]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[24]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[25]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[26]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[27]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[28]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[29]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[30]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[31]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[32]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[33]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[34]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[35]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[36]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[37]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[38]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[39]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[40]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[41]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[42]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[43]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[44]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[45]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[46]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[47]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[48]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[49]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[50]│
└ ┘ ∈ Nonnegatives(1)
Minimize ScalarQuadraticFunction{Float64}:
0.0 - 0.00033855658142679034 x[1] - 0.00045900063043640815 x[2] - 0.0003187675407487563 x[3] - 0.00038643489330353846 x[4] - 0.0011537394365293047 x[5] - 0.0007843124729674312 x[6] - 0.001061249327667408 x[7] - 0.0010449408892289711 x[8] - 0.0006113876921991911 x[9] - 0.0006172044063672302 x[10] - 0.0007772536451186118 x[11] - 0.0008479052793558062 x[12] - 0.00034173154942416297 x[13] - 0.0010986303487154454 x[14] - 0.0006494086085801082 x[15] - 0.0006794986796998539 x[16] - 0.0009660389740328687 x[17] - 0.001166445009616703 x[18] - 0.0004025890560946719 x[19] - 0.0007245375681407701 x[20] - 0.0006273656986263488 x[21] - 0.0007906984988531809 x[22] - 0.0007719816805893664 x[23] - 0.0006079753027788991 x[24] - 0.0009186174293751685 x[25] - 0.0005456152851917019 x[26] - 0.0006353228073856152 x[27] - 0.0011090748443468629 x[28] - 0.0011926048788677207 x[29] - 0.0010268917857414002 x[30] - 0.000978743820799869 x[31] - 0.0011162836887357093 x[32] - 0.0009964056132213991 x[33] - 0.000814858917162367 x[34] - 0.00033977137313870586 x[35] - 0.000633904060604957 x[36] - 0.0007826350307098549 x[37] - 0.00042251188947556805 x[38] - 0.0006285561950168691 x[39] - 0.0003933137671410103 x[40] - 0.0009643841271882351 x[41] - 0.0005399957356685855 x[42] - 0.0007602434742374685 x[43] - 0.0004231245958864945 x[44] - 0.0003386125813757613 x[45] - 0.00118419054979871 x[46] - 0.0009816561459529043 x[47] - 0.0007174408363301076 x[48] - 0.0005053778137232454 x[49] - 0.0006455521149980631 x[50] + 1.0 y[1]² + 1.0 y[2]² + 1.0 y[3]² + 1.0 y[4]² + 1.0 y[5]² + 0.22168311155166154 x[1]² + 1.569674359079319 x[2]² + 1.1253275636203313 x[3]² + 1.958440472561891 x[4]² + 2.1320134751461897 x[5]² + 1.1354989565743618 x[6]² + 1.7659372870351717 x[7]² + 0.1593290841959982 x[8]² + 0.3094227911776114 x[9]² + 0.8791977343224676 x[10]² + 0.39742223612651667 x[11]² + 1.8875918586267313 x[12]² + 1.8387120048986592 x[13]² + 2.190053109789465 x[14]² + 2.1957255604735644 x[15]² + 2.1978762529481384 x[16]² + 1.1710828933547 x[17]² + 1.2987007815595075 x[18]² + 0.281209441224692 x[19]² + 0.33479111624495367 x[20]² + 1.8966897412188368 x[21]² + 1.401948599916701 x[22]² + 2.160159812386103 x[23]² + 1.9353413223067184 x[24]² + 1.8453446813850807 x[25]² + 0.5624261051786525 x[26]² + 1.0198781850630045 x[27]² + 2.0113520898601918 x[28]² + 1.4681359454446885 x[29]² + 0.5963127696051644 x[30]² + 0.5175042820439373 x[31]² + 1.852649196595403 x[32]² + 1.8159596121340185 x[33]² + 0.6715708566047849 x[34]² + 0.546141819204228 x[35]² + 1.7261425935764683 x[36]² + 1.8841597069654406 x[37]² + 1.8282514435305761 x[38]² + 1.9568900128195392 x[39]² + 1.9503256911912632 x[40]² + 1.0526772112820373 x[41]² + 1.0229536502198167 x[42]² + 0.8792148153431698 x[43]² + 2.1254116542837194 x[44]² + 1.7521275518465191 x[45]² + 1.4534148949272803 x[46]² + 0.2944245797695367 x[47]² + 0.2754584682030851 x[48]² + 0.43199283796505494 x[49]² + 2.0761956200923155 x[50]²
Subject to:
VectorAffineFunction{Float64}-in-Zeros
┌ ┐
│0.0 - 0.45836571560595957 x[1] - 1.4882021641049918 x[2] + 2.1826127685114023 x[4] + 0.8239262467380715 x[6] - 1.2962721783934823 x[9] + 0.19983857542320999 x[11] - 1.435940970672912 x[13] + 1.194939742800976 x[18] - 0.7605416579955722 x[19] - 0.10198063634911336 x[20] + 0.0962615513861198 x[23] - 0.12018274708623239 x[26] - 0.7295613191446634 x[27] - 0.07270642655012116 x[28] - 0.8907108705599415 x[29] - 1.0051237161319388 x[30] - 0.8232754710476714 x[31] - 0.3127161299324051 x[32] - 0.7795842203334354 x[34] + 0.9216601059658592 x[35] - 2.069856046894368 x[36] - 0.5189602133669754 x[37] + 0.5885760717502199 x[38] - 0.7196314555287213 x[40] - 0.9291963494383236 x[43] - 0.17796544541790937 x[44] + 0.41792527291699105 x[45] + 0.5159420767895866 x[48] + 1.0 y[1]│
└ ┘ ∈ Zeros(1)
┌ ┐
│0.0 + 0.0503378286805425 x[4] + 1.1256748837213493 x[6] + 0.7658960317180369 x[8] - 0.061035008743322475 x[10] + 0.6046067312789892 x[11] + 1.683500023265881 x[12] + 1.201178638729371 x[13] + 0.6155732499801082 x[14] + 2.4402033735474125 x[23] - 0.7379012770819809 x[24] + 0.20489758707586392 x[25] + 1.2320869079191876 x[26] - 1.9402369852338388 x[27] - 0.954777195400799 x[31] - 0.344798870223836 x[32] + 0.17805576280533475 x[34] + 0.24224089365318544 x[37] - 1.7590069644534676 x[38] + 1.4165151237242104 x[40] + 0.8808123403489245 x[43] - 0.4474817348974519 x[44] + 0.8136739930455366 x[45] + 0.997384476726562 x[47] + 1.0 y[2]│
└ ┘ ∈ Zeros(1)
┌ ┐
│0.0 - 0.20209121321144838 x[1] + 1.157104812420386 x[2] + 0.45265959148235724 x[3] - 0.8009036795569376 x[4] - 2.0302615696038253 x[5] + 0.6241037854724422 x[6] + 0.8271047378482009 x[12] - 1.8249637555191254 x[14] + 0.054713116051507256 x[15] + 1.1115572615284857 x[17] + 1.7828304776409556 x[18] + 0.7423713791628864 x[19] + 0.5552255444433157 x[21] + 0.2303118558750502 x[22] + 0.10973142914455558 x[23] - 0.16181023670093883 x[25] + 1.7265600749058716 x[26] + 1.0154508128378734 x[30] - 0.9272881543745629 x[32] - 0.8528545030926377 x[34] - 0.8887796114735067 x[35] - 0.6372939953316094 x[37] - 2.0729975098289883 x[38] + 0.21793972328895084 x[39] + 0.5968016554494258 x[40] + 0.8446725934201121 x[41] - 0.6564960898033011 x[42] - 0.2577617922174006 x[45] + 1.6066125045474893 x[47] - 0.6106753315638065 x[49] - 0.24094934017892947 x[50] + 1.0 y[3]│
└ ┘ ∈ Zeros(1)
┌ ┐
│0.0 + 0.24314199505818793 x[2] - 1.3876541437893315 x[4] - 0.22683790735634463 x[6] + 0.5214802680235079 x[7] + 1.3354590673591633 x[8] - 1.8504774775149704 x[9] + 0.23051379143328576 x[13] - 0.1572785018821299 x[14] - 1.483039278741509 x[15] - 0.26226284250578463 x[16] - 0.0986696994672989 x[17] - 0.08550126212770054 x[20] + 0.3419778094275683 x[22] + 0.06543821802916351 x[23] - 0.2207564607343709 x[25] - 0.6273452593617963 x[26] + 0.37311820250796757 x[27] - 1.1054210865179164 x[28] + 0.5615671906319677 x[29] - 0.1030742062121358 x[30] - 0.13774215623815417 x[31] + 0.4839037548487663 x[33] + 0.8926885669157067 x[34] - 2.5405468288052515 x[35] + 0.2874685755965493 x[36] - 0.23047583769083854 x[39] + 1.1096979208454745 x[40] + 1.3964654491745603 x[44] - 0.5374828725846994 x[45] + 1.4520935910396786 x[47] + 1.0 y[4]│
└ ┘ ∈ Zeros(1)
┌ ┐
│0.0 - 1.4139342679089253 x[1] - 0.35072192922287954 x[5] + 1.652168425225477 x[7] - 0.049113526881893764 x[18] - 0.8682023381498042 x[22] - 1.5204662064824461 x[23] - 1.3700941514175726 x[24] + 0.05398461169426838 x[25] + 0.013219813753395412 x[26] - 0.8595562201704314 x[31] + 2.3073642877859806 x[33] + 0.0566217713770541 x[35] + 0.12661760952546483 x[40] + 1.4067743147522846 x[41] - 1.2155494239575593 x[43] - 0.24750058660020918 x[47] - 1.7920247650821086 x[49] + 1.0 y[5]│
└ ┘ ∈ Zeros(1)
┌ ┐
│-1.0 + 1.0 x[1] + 1.0 x[2] + 1.0 x[3] + 1.0 x[4] + 1.0 x[5] + 1.0 x[6] + 1.0 x[7] + 1.0 x[8] + 1.0 x[9] + 1.0 x[10] + 1.0 x[11] + 1.0 x[12] + 1.0 x[13] + 1.0 x[14] + 1.0 x[15] + 1.0 x[16] + 1.0 x[17] + 1.0 x[18] + 1.0 x[19] + 1.0 x[20] + 1.0 x[21] + 1.0 x[22] + 1.0 x[23] + 1.0 x[24] + 1.0 x[25] + 1.0 x[26] + 1.0 x[27] + 1.0 x[28] + 1.0 x[29] + 1.0 x[30] + 1.0 x[31] + 1.0 x[32] + 1.0 x[33] + 1.0 x[34] + 1.0 x[35] + 1.0 x[36] + 1.0 x[37] + 1.0 x[38] + 1.0 x[39] + 1.0 x[40] + 1.0 x[41] + 1.0 x[42] + 1.0 x[43] + 1.0 x[44] + 1.0 x[45] + 1.0 x[46] + 1.0 x[47] + 1.0 x[48] + 1.0 x[49] + 1.0 x[50]│
└ ┘ ∈ Zeros(1)
VectorAffineFunction{Float64}-in-Nonnegatives
┌ ┐
│0.0 + 1.0 x[1]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[2]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[3]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[4]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[5]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[6]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[7]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[8]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[9]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[10]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[11]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[12]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[13]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[14]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[15]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[16]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[17]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[18]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[19]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[20]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[21]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[22]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[23]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[24]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[25]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[26]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[27]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[28]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[29]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[30]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[31]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[32]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[33]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[34]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[35]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[36]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[37]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[38]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[39]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[40]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[41]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[42]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[43]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[44]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[45]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[46]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[47]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[48]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[49]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[50]│
└ ┘ ∈ Nonnegatives(1)
Minimize ScalarQuadraticFunction{Float64}:
0.0 - 3.3855658142679034e-5 x[1] - 4.5900063043640815e-5 x[2] - 3.1876754074875626e-5 x[3] - 3.864348933035385e-5 x[4] - 0.00011537394365293046 x[5] - 7.843124729674311e-5 x[6] - 0.0001061249327667408 x[7] - 0.00010449408892289711 x[8] - 6.113876921991911e-5 x[9] - 6.172044063672302e-5 x[10] - 7.772536451186118e-5 x[11] - 8.479052793558062e-5 x[12] - 3.41731549424163e-5 x[13] - 0.00010986303487154455 x[14] - 6.494086085801082e-5 x[15] - 6.794986796998538e-5 x[16] - 9.660389740328688e-5 x[17] - 0.00011664450096167029 x[18] - 4.025890560946719e-5 x[19] - 7.2453756814077e-5 x[20] - 6.273656986263487e-5 x[21] - 7.90698498853181e-5 x[22] - 7.719816805893663e-5 x[23] - 6.079753027788992e-5 x[24] - 9.186174293751685e-5 x[25] - 5.456152851917018e-5 x[26] - 6.353228073856152e-5 x[27] - 0.00011090748443468628 x[28] - 0.00011926048788677207 x[29] - 0.00010268917857414 x[30] - 9.78743820799869e-5 x[31] - 0.00011162836887357093 x[32] - 9.964056132213992e-5 x[33] - 8.14858917162367e-5 x[34] - 3.3977137313870584e-5 x[35] - 6.33904060604957e-5 x[36] - 7.826350307098548e-5 x[37] - 4.2251188947556805e-5 x[38] - 6.285561950168692e-5 x[39] - 3.933137671410103e-5 x[40] - 9.64384127188235e-5 x[41] - 5.3999573566858555e-5 x[42] - 7.602434742374685e-5 x[43] - 4.231245958864945e-5 x[44] - 3.386125813757613e-5 x[45] - 0.00011841905497987099 x[46] - 9.816561459529042e-5 x[47] - 7.174408363301075e-5 x[48] - 5.053778137232454e-5 x[49] - 6.455521149980631e-5 x[50] + 1.0 y[1]² + 1.0 y[2]² + 1.0 y[3]² + 1.0 y[4]² + 1.0 y[5]² + 0.22168311155166154 x[1]² + 1.569674359079319 x[2]² + 1.1253275636203313 x[3]² + 1.958440472561891 x[4]² + 2.1320134751461897 x[5]² + 1.1354989565743618 x[6]² + 1.7659372870351717 x[7]² + 0.1593290841959982 x[8]² + 0.3094227911776114 x[9]² + 0.8791977343224676 x[10]² + 0.39742223612651667 x[11]² + 1.8875918586267313 x[12]² + 1.8387120048986592 x[13]² + 2.190053109789465 x[14]² + 2.1957255604735644 x[15]² + 2.1978762529481384 x[16]² + 1.1710828933547 x[17]² + 1.2987007815595075 x[18]² + 0.281209441224692 x[19]² + 0.33479111624495367 x[20]² + 1.8966897412188368 x[21]² + 1.401948599916701 x[22]² + 2.160159812386103 x[23]² + 1.9353413223067184 x[24]² + 1.8453446813850807 x[25]² + 0.5624261051786525 x[26]² + 1.0198781850630045 x[27]² + 2.0113520898601918 x[28]² + 1.4681359454446885 x[29]² + 0.5963127696051644 x[30]² + 0.5175042820439373 x[31]² + 1.852649196595403 x[32]² + 1.8159596121340185 x[33]² + 0.6715708566047849 x[34]² + 0.546141819204228 x[35]² + 1.7261425935764683 x[36]² + 1.8841597069654406 x[37]² + 1.8282514435305761 x[38]² + 1.9568900128195392 x[39]² + 1.9503256911912632 x[40]² + 1.0526772112820373 x[41]² + 1.0229536502198167 x[42]² + 0.8792148153431698 x[43]² + 2.1254116542837194 x[44]² + 1.7521275518465191 x[45]² + 1.4534148949272803 x[46]² + 0.2944245797695367 x[47]² + 0.2754584682030851 x[48]² + 0.43199283796505494 x[49]² + 2.0761956200923155 x[50]²
Subject to:
VectorAffineFunction{Float64}-in-Zeros
┌ ┐
│0.0 - 0.45836571560595957 x[1] - 1.4882021641049918 x[2] + 2.1826127685114023 x[4] + 0.8239262467380715 x[6] - 1.2962721783934823 x[9] + 0.19983857542320999 x[11] - 1.435940970672912 x[13] + 1.194939742800976 x[18] - 0.7605416579955722 x[19] - 0.10198063634911336 x[20] + 0.0962615513861198 x[23] - 0.12018274708623239 x[26] - 0.7295613191446634 x[27] - 0.07270642655012116 x[28] - 0.8907108705599415 x[29] - 1.0051237161319388 x[30] - 0.8232754710476714 x[31] - 0.3127161299324051 x[32] - 0.7795842203334354 x[34] + 0.9216601059658592 x[35] - 2.069856046894368 x[36] - 0.5189602133669754 x[37] + 0.5885760717502199 x[38] - 0.7196314555287213 x[40] - 0.9291963494383236 x[43] - 0.17796544541790937 x[44] + 0.41792527291699105 x[45] + 0.5159420767895866 x[48] + 1.0 y[1]│
└ ┘ ∈ Zeros(1)
┌ ┐
│0.0 + 0.0503378286805425 x[4] + 1.1256748837213493 x[6] + 0.7658960317180369 x[8] - 0.061035008743322475 x[10] + 0.6046067312789892 x[11] + 1.683500023265881 x[12] + 1.201178638729371 x[13] + 0.6155732499801082 x[14] + 2.4402033735474125 x[23] - 0.7379012770819809 x[24] + 0.20489758707586392 x[25] + 1.2320869079191876 x[26] - 1.9402369852338388 x[27] - 0.954777195400799 x[31] - 0.344798870223836 x[32] + 0.17805576280533475 x[34] + 0.24224089365318544 x[37] - 1.7590069644534676 x[38] + 1.4165151237242104 x[40] + 0.8808123403489245 x[43] - 0.4474817348974519 x[44] + 0.8136739930455366 x[45] + 0.997384476726562 x[47] + 1.0 y[2]│
└ ┘ ∈ Zeros(1)
┌ ┐
│0.0 - 0.20209121321144838 x[1] + 1.157104812420386 x[2] + 0.45265959148235724 x[3] - 0.8009036795569376 x[4] - 2.0302615696038253 x[5] + 0.6241037854724422 x[6] + 0.8271047378482009 x[12] - 1.8249637555191254 x[14] + 0.054713116051507256 x[15] + 1.1115572615284857 x[17] + 1.7828304776409556 x[18] + 0.7423713791628864 x[19] + 0.5552255444433157 x[21] + 0.2303118558750502 x[22] + 0.10973142914455558 x[23] - 0.16181023670093883 x[25] + 1.7265600749058716 x[26] + 1.0154508128378734 x[30] - 0.9272881543745629 x[32] - 0.8528545030926377 x[34] - 0.8887796114735067 x[35] - 0.6372939953316094 x[37] - 2.0729975098289883 x[38] + 0.21793972328895084 x[39] + 0.5968016554494258 x[40] + 0.8446725934201121 x[41] - 0.6564960898033011 x[42] - 0.2577617922174006 x[45] + 1.6066125045474893 x[47] - 0.6106753315638065 x[49] - 0.24094934017892947 x[50] + 1.0 y[3]│
└ ┘ ∈ Zeros(1)
┌ ┐
│0.0 + 0.24314199505818793 x[2] - 1.3876541437893315 x[4] - 0.22683790735634463 x[6] + 0.5214802680235079 x[7] + 1.3354590673591633 x[8] - 1.8504774775149704 x[9] + 0.23051379143328576 x[13] - 0.1572785018821299 x[14] - 1.483039278741509 x[15] - 0.26226284250578463 x[16] - 0.0986696994672989 x[17] - 0.08550126212770054 x[20] + 0.3419778094275683 x[22] + 0.06543821802916351 x[23] - 0.2207564607343709 x[25] - 0.6273452593617963 x[26] + 0.37311820250796757 x[27] - 1.1054210865179164 x[28] + 0.5615671906319677 x[29] - 0.1030742062121358 x[30] - 0.13774215623815417 x[31] + 0.4839037548487663 x[33] + 0.8926885669157067 x[34] - 2.5405468288052515 x[35] + 0.2874685755965493 x[36] - 0.23047583769083854 x[39] + 1.1096979208454745 x[40] + 1.3964654491745603 x[44] - 0.5374828725846994 x[45] + 1.4520935910396786 x[47] + 1.0 y[4]│
└ ┘ ∈ Zeros(1)
┌ ┐
│0.0 - 1.4139342679089253 x[1] - 0.35072192922287954 x[5] + 1.652168425225477 x[7] - 0.049113526881893764 x[18] - 0.8682023381498042 x[22] - 1.5204662064824461 x[23] - 1.3700941514175726 x[24] + 0.05398461169426838 x[25] + 0.013219813753395412 x[26] - 0.8595562201704314 x[31] + 2.3073642877859806 x[33] + 0.0566217713770541 x[35] + 0.12661760952546483 x[40] + 1.4067743147522846 x[41] - 1.2155494239575593 x[43] - 0.24750058660020918 x[47] - 1.7920247650821086 x[49] + 1.0 y[5]│
└ ┘ ∈ Zeros(1)
┌ ┐
│-1.0 + 1.0 x[1] + 1.0 x[2] + 1.0 x[3] + 1.0 x[4] + 1.0 x[5] + 1.0 x[6] + 1.0 x[7] + 1.0 x[8] + 1.0 x[9] + 1.0 x[10] + 1.0 x[11] + 1.0 x[12] + 1.0 x[13] + 1.0 x[14] + 1.0 x[15] + 1.0 x[16] + 1.0 x[17] + 1.0 x[18] + 1.0 x[19] + 1.0 x[20] + 1.0 x[21] + 1.0 x[22] + 1.0 x[23] + 1.0 x[24] + 1.0 x[25] + 1.0 x[26] + 1.0 x[27] + 1.0 x[28] + 1.0 x[29] + 1.0 x[30] + 1.0 x[31] + 1.0 x[32] + 1.0 x[33] + 1.0 x[34] + 1.0 x[35] + 1.0 x[36] + 1.0 x[37] + 1.0 x[38] + 1.0 x[39] + 1.0 x[40] + 1.0 x[41] + 1.0 x[42] + 1.0 x[43] + 1.0 x[44] + 1.0 x[45] + 1.0 x[46] + 1.0 x[47] + 1.0 x[48] + 1.0 x[49] + 1.0 x[50]│
└ ┘ ∈ Zeros(1)
VectorAffineFunction{Float64}-in-Nonnegatives
┌ ┐
│0.0 + 1.0 x[1]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[2]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[3]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[4]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[5]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[6]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[7]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[8]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[9]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[10]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[11]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[12]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[13]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[14]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[15]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[16]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[17]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[18]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[19]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[20]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[21]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[22]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[23]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[24]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[25]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[26]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[27]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[28]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[29]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[30]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[31]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[32]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[33]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[34]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[35]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[36]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[37]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[38]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[39]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[40]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[41]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[42]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[43]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[44]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[45]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[46]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[47]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[48]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[49]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[50]│
└ ┘ ∈ Nonnegatives(1)We can now plot the risk-return trade-off curve:
using Plots
Plots.plot(risks, returns, xlabel = "Standard deviation (risk)", ylabel = "Expected return", title = "Risk-return trade-off for efficient portfolios", legend = false)
When the model is updated in JuMP as above the JuMP.model is copied in full to COSMO. We are trying to improve the interface with respect to model updates in the future. Until then you can use Model Updates in COSMOs native interface.
Transaction costs
In the model above we assume that trading the assets is free and does not impact the market. However, this is clearly not the case in reality. To make the example more realistic consider the following cost $c_j$ associated with the trade $δ_j = x_j - x_j^0$:
\[c_j(\delta_j) = a_j |\delta_j| + b_j |\delta_j|^{3/2},\]
where the first term models the bid-ask spread and broker fees for asset $j$. The second term models the impact on the market that our trade has. This is obviously only a factor if the volume of our trade is significant. The constant $b_j$ is a function of the total volume traded in the considered time periode and the price volatility of the asset and has to be estimated by the trader. To make this example simple we consider the same coefficients $a$ and $b$ for every asset. The $|\delta_j|^{3/2}$ term can be easily modeled using a power cone constraint $\mathcal{K}_{pow} = \{(x, y, z) \mid x^\alpha y^{(1-\alpha)} \geq |z|, x \geq 0, y \geq 0, 0 \leq \alpha \leq 1 \}$. In fact this can be used to model any market impact function with exponent greater than 1. We can write the total transaction cost $a^\top s + b^\top t$ where $s_j$ bounds the absolute value of $\delta_j$ and $t_{j}$ is used to bound the term $|x_j - x_j^0|^{3/2} \leq t_{j}$ using a power cone formulation: $(t_{j}, 1, x_j - x_j^0) \in \mathcal{K}_{pow}(2/3)$.
a = 1e-3
b = 1e-1
γ = 1.0;
model = JuMP.Model(optimizer_with_attributes(COSMO.Optimizer, "eps_abs" => 1e-5, "eps_rel" => 1e-5));
@variable(model, x[1:n]);
@variable(model, y[1:k]);
@variable(model, t[1:n]);
@variable(model, s[1:n]);
@objective(model, Min, x' * D * x + y' * y - 1/γ * μ' * x);
@constraint(model, y .== F' * x);
@constraint(model, x .>= 0);
# transaction costs
@constraint(model, sum(x) + a * sum(s) + b * sum(t) == d + sum(x0) );
@constraint(model, [i = 1:n], x[i] - x0[i] <= s[i]); # model the absolute value with slack variable s
@constraint(model, [i = 1:n], x0[i] - x[i] <= s[i]);
@constraint(model, [i = 1:n], [t[i], 1, x[i] - x0[i]] in MOI.PowerCone(2/3));
JuMP.optimize!(model)Minimize ScalarQuadraticFunction{Float64}:
0.0 - 0.03385565814267903 x[1] - 0.04590006304364081 x[2] - 0.03187675407487563 x[3] - 0.038643489330353845 x[4] - 0.11537394365293047 x[5] - 0.07843124729674311 x[6] - 0.1061249327667408 x[7] - 0.10449408892289712 x[8] - 0.06113876921991911 x[9] - 0.061720440636723016 x[10] - 0.07772536451186118 x[11] - 0.08479052793558062 x[12] - 0.034173154942416295 x[13] - 0.10986303487154454 x[14] - 0.06494086085801082 x[15] - 0.06794986796998538 x[16] - 0.09660389740328687 x[17] - 0.11664450096167028 x[18] - 0.04025890560946719 x[19] - 0.07245375681407701 x[20] - 0.06273656986263487 x[21] - 0.0790698498853181 x[22] - 0.07719816805893663 x[23] - 0.060797530277889915 x[24] - 0.09186174293751685 x[25] - 0.054561528519170184 x[26] - 0.06353228073856151 x[27] - 0.11090748443468627 x[28] - 0.11926048788677207 x[29] - 0.10268917857414 x[30] - 0.0978743820799869 x[31] - 0.11162836887357093 x[32] - 0.09964056132213991 x[33] - 0.0814858917162367 x[34] - 0.03397713731387059 x[35] - 0.06339040606049569 x[36] - 0.07826350307098548 x[37] - 0.042251188947556806 x[38] - 0.06285561950168692 x[39] - 0.03933137671410103 x[40] - 0.0964384127188235 x[41] - 0.053999573566858555 x[42] - 0.07602434742374685 x[43] - 0.042312459588649445 x[44] - 0.03386125813757613 x[45] - 0.11841905497987099 x[46] - 0.09816561459529043 x[47] - 0.07174408363301076 x[48] - 0.050537781372324536 x[49] - 0.06455521149980631 x[50] + 1.0 y[1]² + 1.0 y[2]² + 1.0 y[3]² + 1.0 y[4]² + 1.0 y[5]² + 0.22168311155166154 x[1]² + 1.569674359079319 x[2]² + 1.1253275636203313 x[3]² + 1.958440472561891 x[4]² + 2.1320134751461897 x[5]² + 1.1354989565743618 x[6]² + 1.7659372870351717 x[7]² + 0.1593290841959982 x[8]² + 0.3094227911776114 x[9]² + 0.8791977343224676 x[10]² + 0.39742223612651667 x[11]² + 1.8875918586267313 x[12]² + 1.8387120048986592 x[13]² + 2.190053109789465 x[14]² + 2.1957255604735644 x[15]² + 2.1978762529481384 x[16]² + 1.1710828933547 x[17]² + 1.2987007815595075 x[18]² + 0.281209441224692 x[19]² + 0.33479111624495367 x[20]² + 1.8966897412188368 x[21]² + 1.401948599916701 x[22]² + 2.160159812386103 x[23]² + 1.9353413223067184 x[24]² + 1.8453446813850807 x[25]² + 0.5624261051786525 x[26]² + 1.0198781850630045 x[27]² + 2.0113520898601918 x[28]² + 1.4681359454446885 x[29]² + 0.5963127696051644 x[30]² + 0.5175042820439373 x[31]² + 1.852649196595403 x[32]² + 1.8159596121340185 x[33]² + 0.6715708566047849 x[34]² + 0.546141819204228 x[35]² + 1.7261425935764683 x[36]² + 1.8841597069654406 x[37]² + 1.8282514435305761 x[38]² + 1.9568900128195392 x[39]² + 1.9503256911912632 x[40]² + 1.0526772112820373 x[41]² + 1.0229536502198167 x[42]² + 0.8792148153431698 x[43]² + 2.1254116542837194 x[44]² + 1.7521275518465191 x[45]² + 1.4534148949272803 x[46]² + 0.2944245797695367 x[47]² + 0.2754584682030851 x[48]² + 0.43199283796505494 x[49]² + 2.0761956200923155 x[50]²
Subject to:
VectorAffineFunction{Float64}-in-Zeros
┌ ┐
│0.0 - 0.45836571560595957 x[1] - 1.4882021641049918 x[2] + 2.1826127685114023 x[4] + 0.8239262467380715 x[6] - 1.2962721783934823 x[9] + 0.19983857542320999 x[11] - 1.435940970672912 x[13] + 1.194939742800976 x[18] - 0.7605416579955722 x[19] - 0.10198063634911336 x[20] + 0.0962615513861198 x[23] - 0.12018274708623239 x[26] - 0.7295613191446634 x[27] - 0.07270642655012116 x[28] - 0.8907108705599415 x[29] - 1.0051237161319388 x[30] - 0.8232754710476714 x[31] - 0.3127161299324051 x[32] - 0.7795842203334354 x[34] + 0.9216601059658592 x[35] - 2.069856046894368 x[36] - 0.5189602133669754 x[37] + 0.5885760717502199 x[38] - 0.7196314555287213 x[40] - 0.9291963494383236 x[43] - 0.17796544541790937 x[44] + 0.41792527291699105 x[45] + 0.5159420767895866 x[48] + 1.0 y[1]│
└ ┘ ∈ Zeros(1)
┌ ┐
│0.0 + 0.0503378286805425 x[4] + 1.1256748837213493 x[6] + 0.7658960317180369 x[8] - 0.061035008743322475 x[10] + 0.6046067312789892 x[11] + 1.683500023265881 x[12] + 1.201178638729371 x[13] + 0.6155732499801082 x[14] + 2.4402033735474125 x[23] - 0.7379012770819809 x[24] + 0.20489758707586392 x[25] + 1.2320869079191876 x[26] - 1.9402369852338388 x[27] - 0.954777195400799 x[31] - 0.344798870223836 x[32] + 0.17805576280533475 x[34] + 0.24224089365318544 x[37] - 1.7590069644534676 x[38] + 1.4165151237242104 x[40] + 0.8808123403489245 x[43] - 0.4474817348974519 x[44] + 0.8136739930455366 x[45] + 0.997384476726562 x[47] + 1.0 y[2]│
└ ┘ ∈ Zeros(1)
┌ ┐
│0.0 - 0.20209121321144838 x[1] + 1.157104812420386 x[2] + 0.45265959148235724 x[3] - 0.8009036795569376 x[4] - 2.0302615696038253 x[5] + 0.6241037854724422 x[6] + 0.8271047378482009 x[12] - 1.8249637555191254 x[14] + 0.054713116051507256 x[15] + 1.1115572615284857 x[17] + 1.7828304776409556 x[18] + 0.7423713791628864 x[19] + 0.5552255444433157 x[21] + 0.2303118558750502 x[22] + 0.10973142914455558 x[23] - 0.16181023670093883 x[25] + 1.7265600749058716 x[26] + 1.0154508128378734 x[30] - 0.9272881543745629 x[32] - 0.8528545030926377 x[34] - 0.8887796114735067 x[35] - 0.6372939953316094 x[37] - 2.0729975098289883 x[38] + 0.21793972328895084 x[39] + 0.5968016554494258 x[40] + 0.8446725934201121 x[41] - 0.6564960898033011 x[42] - 0.2577617922174006 x[45] + 1.6066125045474893 x[47] - 0.6106753315638065 x[49] - 0.24094934017892947 x[50] + 1.0 y[3]│
└ ┘ ∈ Zeros(1)
┌ ┐
│0.0 + 0.24314199505818793 x[2] - 1.3876541437893315 x[4] - 0.22683790735634463 x[6] + 0.5214802680235079 x[7] + 1.3354590673591633 x[8] - 1.8504774775149704 x[9] + 0.23051379143328576 x[13] - 0.1572785018821299 x[14] - 1.483039278741509 x[15] - 0.26226284250578463 x[16] - 0.0986696994672989 x[17] - 0.08550126212770054 x[20] + 0.3419778094275683 x[22] + 0.06543821802916351 x[23] - 0.2207564607343709 x[25] - 0.6273452593617963 x[26] + 0.37311820250796757 x[27] - 1.1054210865179164 x[28] + 0.5615671906319677 x[29] - 0.1030742062121358 x[30] - 0.13774215623815417 x[31] + 0.4839037548487663 x[33] + 0.8926885669157067 x[34] - 2.5405468288052515 x[35] + 0.2874685755965493 x[36] - 0.23047583769083854 x[39] + 1.1096979208454745 x[40] + 1.3964654491745603 x[44] - 0.5374828725846994 x[45] + 1.4520935910396786 x[47] + 1.0 y[4]│
└ ┘ ∈ Zeros(1)
┌ ┐
│0.0 - 1.4139342679089253 x[1] - 0.35072192922287954 x[5] + 1.652168425225477 x[7] - 0.049113526881893764 x[18] - 0.8682023381498042 x[22] - 1.5204662064824461 x[23] - 1.3700941514175726 x[24] + 0.05398461169426838 x[25] + 0.013219813753395412 x[26] - 0.8595562201704314 x[31] + 2.3073642877859806 x[33] + 0.0566217713770541 x[35] + 0.12661760952546483 x[40] + 1.4067743147522846 x[41] - 1.2155494239575593 x[43] - 0.24750058660020918 x[47] - 1.7920247650821086 x[49] + 1.0 y[5]│
└ ┘ ∈ Zeros(1)
┌ ┐
│-1.0 + 1.0 x[1] + 1.0 x[2] + 1.0 x[3] + 1.0 x[4] + 1.0 x[5] + 1.0 x[6] + 1.0 x[7] + 1.0 x[8] + 1.0 x[9] + 1.0 x[10] + 1.0 x[11] + 1.0 x[12] + 1.0 x[13] + 1.0 x[14] + 1.0 x[15] + 1.0 x[16] + 1.0 x[17] + 1.0 x[18] + 1.0 x[19] + 1.0 x[20] + 1.0 x[21] + 1.0 x[22] + 1.0 x[23] + 1.0 x[24] + 1.0 x[25] + 1.0 x[26] + 1.0 x[27] + 1.0 x[28] + 1.0 x[29] + 1.0 x[30] + 1.0 x[31] + 1.0 x[32] + 1.0 x[33] + 1.0 x[34] + 1.0 x[35] + 1.0 x[36] + 1.0 x[37] + 1.0 x[38] + 1.0 x[39] + 1.0 x[40] + 1.0 x[41] + 1.0 x[42] + 1.0 x[43] + 1.0 x[44] + 1.0 x[45] + 1.0 x[46] + 1.0 x[47] + 1.0 x[48] + 1.0 x[49] + 1.0 x[50] + 0.1 t[1] + 0.1 t[2] + 0.1 t[3] + 0.1 t[4] + 0.1 t[5] + 0.1 t[6] + 0.1 t[7] + 0.1 t[8] + 0.1 t[9] + 0.1 t[10] + 0.1 t[11] + 0.1 t[12] + 0.1 t[13] + 0.1 t[14] + 0.1 t[15] + 0.1 t[16] + 0.1 t[17] + 0.1 t[18] + 0.1 t[19] + 0.1 t[20] + 0.1 t[21] + 0.1 t[22] + 0.1 t[23] + 0.1 t[24] + 0.1 t[25] + 0.1 t[26] + 0.1 t[27] + 0.1 t[28] + 0.1 t[29] + 0.1 t[30] + 0.1 t[31] + 0.1 t[32] + 0.1 t[33] + 0.1 t[34] + 0.1 t[35] + 0.1 t[36] + 0.1 t[37] + 0.1 t[38] + 0.1 t[39] + 0.1 t[40] + 0.1 t[41] + 0.1 t[42] + 0.1 t[43] + 0.1 t[44] + 0.1 t[45] + 0.1 t[46] + 0.1 t[47] + 0.1 t[48] + 0.1 t[49] + 0.1 t[50] + 0.001 s[1] + 0.001 s[2] + 0.001 s[3] + 0.001 s[4] + 0.001 s[5] + 0.001 s[6] + 0.001 s[7] + 0.001 s[8] + 0.001 s[9] + 0.001 s[10] + 0.001 s[11] + 0.001 s[12] + 0.001 s[13] + 0.001 s[14] + 0.001 s[15] + 0.001 s[16] + 0.001 s[17] + 0.001 s[18] + 0.001 s[19] + 0.001 s[20] + 0.001 s[21] + 0.001 s[22] + 0.001 s[23] + 0.001 s[24] + 0.001 s[25] + 0.001 s[26] + 0.001 s[27] + 0.001 s[28] + 0.001 s[29] + 0.001 s[30] + 0.001 s[31] + 0.001 s[32] + 0.001 s[33] + 0.001 s[34] + 0.001 s[35] + 0.001 s[36] + 0.001 s[37] + 0.001 s[38] + 0.001 s[39] + 0.001 s[40] + 0.001 s[41] + 0.001 s[42] + 0.001 s[43] + 0.001 s[44] + 0.001 s[45] + 0.001 s[46] + 0.001 s[47] + 0.001 s[48] + 0.001 s[49] + 0.001 s[50]│
└ ┘ ∈ Zeros(1)
VectorAffineFunction{Float64}-in-Nonnegatives
┌ ┐
│0.0 + 1.0 x[1]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[2]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[3]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[4]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[5]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[6]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[7]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[8]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[9]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[10]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[11]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[12]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[13]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[14]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[15]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[16]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[17]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[18]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[19]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[20]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[21]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[22]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[23]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[24]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[25]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[26]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[27]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[28]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[29]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[30]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[31]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[32]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[33]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[34]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[35]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[36]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[37]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[38]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[39]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[40]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[41]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[42]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[43]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[44]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[45]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[46]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[47]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[48]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[49]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[50]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 - 1.0 x[1] + 1.0 s[1]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 - 1.0 x[2] + 1.0 s[2]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 - 1.0 x[3] + 1.0 s[3]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 - 1.0 x[4] + 1.0 s[4]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 - 1.0 x[5] + 1.0 s[5]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 - 1.0 x[6] + 1.0 s[6]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 - 1.0 x[7] + 1.0 s[7]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 - 1.0 x[8] + 1.0 s[8]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 - 1.0 x[9] + 1.0 s[9]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 - 1.0 x[10] + 1.0 s[10]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 - 1.0 x[11] + 1.0 s[11]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 - 1.0 x[12] + 1.0 s[12]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 - 1.0 x[13] + 1.0 s[13]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 - 1.0 x[14] + 1.0 s[14]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 - 1.0 x[15] + 1.0 s[15]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 - 1.0 x[16] + 1.0 s[16]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 - 1.0 x[17] + 1.0 s[17]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 - 1.0 x[18] + 1.0 s[18]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 - 1.0 x[19] + 1.0 s[19]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 - 1.0 x[20] + 1.0 s[20]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 - 1.0 x[21] + 1.0 s[21]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 - 1.0 x[22] + 1.0 s[22]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 - 1.0 x[23] + 1.0 s[23]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 - 1.0 x[24] + 1.0 s[24]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 - 1.0 x[25] + 1.0 s[25]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 - 1.0 x[26] + 1.0 s[26]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 - 1.0 x[27] + 1.0 s[27]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 - 1.0 x[28] + 1.0 s[28]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 - 1.0 x[29] + 1.0 s[29]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 - 1.0 x[30] + 1.0 s[30]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 - 1.0 x[31] + 1.0 s[31]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 - 1.0 x[32] + 1.0 s[32]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 - 1.0 x[33] + 1.0 s[33]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 - 1.0 x[34] + 1.0 s[34]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 - 1.0 x[35] + 1.0 s[35]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 - 1.0 x[36] + 1.0 s[36]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 - 1.0 x[37] + 1.0 s[37]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 - 1.0 x[38] + 1.0 s[38]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 - 1.0 x[39] + 1.0 s[39]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 - 1.0 x[40] + 1.0 s[40]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 - 1.0 x[41] + 1.0 s[41]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 - 1.0 x[42] + 1.0 s[42]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 - 1.0 x[43] + 1.0 s[43]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 - 1.0 x[44] + 1.0 s[44]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 - 1.0 x[45] + 1.0 s[45]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 - 1.0 x[46] + 1.0 s[46]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 - 1.0 x[47] + 1.0 s[47]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 - 1.0 x[48] + 1.0 s[48]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 - 1.0 x[49] + 1.0 s[49]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 - 1.0 x[50] + 1.0 s[50]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[1] + 1.0 s[1]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[2] + 1.0 s[2]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[3] + 1.0 s[3]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[4] + 1.0 s[4]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[5] + 1.0 s[5]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[6] + 1.0 s[6]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[7] + 1.0 s[7]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[8] + 1.0 s[8]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[9] + 1.0 s[9]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[10] + 1.0 s[10]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[11] + 1.0 s[11]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[12] + 1.0 s[12]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[13] + 1.0 s[13]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[14] + 1.0 s[14]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[15] + 1.0 s[15]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[16] + 1.0 s[16]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[17] + 1.0 s[17]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[18] + 1.0 s[18]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[19] + 1.0 s[19]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[20] + 1.0 s[20]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[21] + 1.0 s[21]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[22] + 1.0 s[22]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[23] + 1.0 s[23]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[24] + 1.0 s[24]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[25] + 1.0 s[25]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[26] + 1.0 s[26]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[27] + 1.0 s[27]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[28] + 1.0 s[28]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[29] + 1.0 s[29]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[30] + 1.0 s[30]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[31] + 1.0 s[31]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[32] + 1.0 s[32]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[33] + 1.0 s[33]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[34] + 1.0 s[34]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[35] + 1.0 s[35]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[36] + 1.0 s[36]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[37] + 1.0 s[37]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[38] + 1.0 s[38]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[39] + 1.0 s[39]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[40] + 1.0 s[40]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[41] + 1.0 s[41]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[42] + 1.0 s[42]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[43] + 1.0 s[43]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[44] + 1.0 s[44]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[45] + 1.0 s[45]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[46] + 1.0 s[46]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[47] + 1.0 s[47]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[48] + 1.0 s[48]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[49] + 1.0 s[49]│
└ ┘ ∈ Nonnegatives(1)
┌ ┐
│0.0 + 1.0 x[50] + 1.0 s[50]│
└ ┘ ∈ Nonnegatives(1)
VectorAffineFunction{Float64}-in-PowerCone{Float64}
┌ ┐
│0.0 + 1.0 t[1] │
│1.0 │
│-0.0 + 1.0 x[1]│
└ ┘ ∈ PowerCone{Float64}(0.6666666666666666)
┌ ┐
│0.0 + 1.0 t[2] │
│1.0 │
│-0.0 + 1.0 x[2]│
└ ┘ ∈ PowerCone{Float64}(0.6666666666666666)
┌ ┐
│0.0 + 1.0 t[3] │
│1.0 │
│-0.0 + 1.0 x[3]│
└ ┘ ∈ PowerCone{Float64}(0.6666666666666666)
┌ ┐
│0.0 + 1.0 t[4] │
│1.0 │
│-0.0 + 1.0 x[4]│
└ ┘ ∈ PowerCone{Float64}(0.6666666666666666)
┌ ┐
│0.0 + 1.0 t[5] │
│1.0 │
│-0.0 + 1.0 x[5]│
└ ┘ ∈ PowerCone{Float64}(0.6666666666666666)
┌ ┐
│0.0 + 1.0 t[6] │
│1.0 │
│-0.0 + 1.0 x[6]│
└ ┘ ∈ PowerCone{Float64}(0.6666666666666666)
┌ ┐
│0.0 + 1.0 t[7] │
│1.0 │
│-0.0 + 1.0 x[7]│
└ ┘ ∈ PowerCone{Float64}(0.6666666666666666)
┌ ┐
│0.0 + 1.0 t[8] │
│1.0 │
│-0.0 + 1.0 x[8]│
└ ┘ ∈ PowerCone{Float64}(0.6666666666666666)
┌ ┐
│0.0 + 1.0 t[9] │
│1.0 │
│-0.0 + 1.0 x[9]│
└ ┘ ∈ PowerCone{Float64}(0.6666666666666666)
┌ ┐
│0.0 + 1.0 t[10] │
│1.0 │
│-0.0 + 1.0 x[10]│
└ ┘ ∈ PowerCone{Float64}(0.6666666666666666)
┌ ┐
│0.0 + 1.0 t[11] │
│1.0 │
│-0.0 + 1.0 x[11]│
└ ┘ ∈ PowerCone{Float64}(0.6666666666666666)
┌ ┐
│0.0 + 1.0 t[12] │
│1.0 │
│-0.0 + 1.0 x[12]│
└ ┘ ∈ PowerCone{Float64}(0.6666666666666666)
┌ ┐
│0.0 + 1.0 t[13] │
│1.0 │
│-0.0 + 1.0 x[13]│
└ ┘ ∈ PowerCone{Float64}(0.6666666666666666)
┌ ┐
│0.0 + 1.0 t[14] │
│1.0 │
│-0.0 + 1.0 x[14]│
└ ┘ ∈ PowerCone{Float64}(0.6666666666666666)
┌ ┐
│0.0 + 1.0 t[15] │
│1.0 │
│-0.0 + 1.0 x[15]│
└ ┘ ∈ PowerCone{Float64}(0.6666666666666666)
┌ ┐
│0.0 + 1.0 t[16] │
│1.0 │
│-0.0 + 1.0 x[16]│
└ ┘ ∈ PowerCone{Float64}(0.6666666666666666)
┌ ┐
│0.0 + 1.0 t[17] │
│1.0 │
│-0.0 + 1.0 x[17]│
└ ┘ ∈ PowerCone{Float64}(0.6666666666666666)
┌ ┐
│0.0 + 1.0 t[18] │
│1.0 │
│-0.0 + 1.0 x[18]│
└ ┘ ∈ PowerCone{Float64}(0.6666666666666666)
┌ ┐
│0.0 + 1.0 t[19] │
│1.0 │
│-0.0 + 1.0 x[19]│
└ ┘ ∈ PowerCone{Float64}(0.6666666666666666)
┌ ┐
│0.0 + 1.0 t[20] │
│1.0 │
│-0.0 + 1.0 x[20]│
└ ┘ ∈ PowerCone{Float64}(0.6666666666666666)
┌ ┐
│0.0 + 1.0 t[21] │
│1.0 │
│-0.0 + 1.0 x[21]│
└ ┘ ∈ PowerCone{Float64}(0.6666666666666666)
┌ ┐
│0.0 + 1.0 t[22] │
│1.0 │
│-0.0 + 1.0 x[22]│
└ ┘ ∈ PowerCone{Float64}(0.6666666666666666)
┌ ┐
│0.0 + 1.0 t[23] │
│1.0 │
│-0.0 + 1.0 x[23]│
└ ┘ ∈ PowerCone{Float64}(0.6666666666666666)
┌ ┐
│0.0 + 1.0 t[24] │
│1.0 │
│-0.0 + 1.0 x[24]│
└ ┘ ∈ PowerCone{Float64}(0.6666666666666666)
┌ ┐
│0.0 + 1.0 t[25] │
│1.0 │
│-0.0 + 1.0 x[25]│
└ ┘ ∈ PowerCone{Float64}(0.6666666666666666)
┌ ┐
│0.0 + 1.0 t[26] │
│1.0 │
│-0.0 + 1.0 x[26]│
└ ┘ ∈ PowerCone{Float64}(0.6666666666666666)
┌ ┐
│0.0 + 1.0 t[27] │
│1.0 │
│-0.0 + 1.0 x[27]│
└ ┘ ∈ PowerCone{Float64}(0.6666666666666666)
┌ ┐
│0.0 + 1.0 t[28] │
│1.0 │
│-0.0 + 1.0 x[28]│
└ ┘ ∈ PowerCone{Float64}(0.6666666666666666)
┌ ┐
│0.0 + 1.0 t[29] │
│1.0 │
│-0.0 + 1.0 x[29]│
└ ┘ ∈ PowerCone{Float64}(0.6666666666666666)
┌ ┐
│0.0 + 1.0 t[30] │
│1.0 │
│-0.0 + 1.0 x[30]│
└ ┘ ∈ PowerCone{Float64}(0.6666666666666666)
┌ ┐
│0.0 + 1.0 t[31] │
│1.0 │
│-0.0 + 1.0 x[31]│
└ ┘ ∈ PowerCone{Float64}(0.6666666666666666)
┌ ┐
│0.0 + 1.0 t[32] │
│1.0 │
│-0.0 + 1.0 x[32]│
└ ┘ ∈ PowerCone{Float64}(0.6666666666666666)
┌ ┐
│0.0 + 1.0 t[33] │
│1.0 │
│-0.0 + 1.0 x[33]│
└ ┘ ∈ PowerCone{Float64}(0.6666666666666666)
┌ ┐
│0.0 + 1.0 t[34] │
│1.0 │
│-0.0 + 1.0 x[34]│
└ ┘ ∈ PowerCone{Float64}(0.6666666666666666)
┌ ┐
│0.0 + 1.0 t[35] │
│1.0 │
│-0.0 + 1.0 x[35]│
└ ┘ ∈ PowerCone{Float64}(0.6666666666666666)
┌ ┐
│0.0 + 1.0 t[36] │
│1.0 │
│-0.0 + 1.0 x[36]│
└ ┘ ∈ PowerCone{Float64}(0.6666666666666666)
┌ ┐
│0.0 + 1.0 t[37] │
│1.0 │
│-0.0 + 1.0 x[37]│
└ ┘ ∈ PowerCone{Float64}(0.6666666666666666)
┌ ┐
│0.0 + 1.0 t[38] │
│1.0 │
│-0.0 + 1.0 x[38]│
└ ┘ ∈ PowerCone{Float64}(0.6666666666666666)
┌ ┐
│0.0 + 1.0 t[39] │
│1.0 │
│-0.0 + 1.0 x[39]│
└ ┘ ∈ PowerCone{Float64}(0.6666666666666666)
┌ ┐
│0.0 + 1.0 t[40] │
│1.0 │
│-0.0 + 1.0 x[40]│
└ ┘ ∈ PowerCone{Float64}(0.6666666666666666)
┌ ┐
│0.0 + 1.0 t[41] │
│1.0 │
│-0.0 + 1.0 x[41]│
└ ┘ ∈ PowerCone{Float64}(0.6666666666666666)
┌ ┐
│0.0 + 1.0 t[42] │
│1.0 │
│-0.0 + 1.0 x[42]│
└ ┘ ∈ PowerCone{Float64}(0.6666666666666666)
┌ ┐
│0.0 + 1.0 t[43] │
│1.0 │
│-0.0 + 1.0 x[43]│
└ ┘ ∈ PowerCone{Float64}(0.6666666666666666)
┌ ┐
│0.0 + 1.0 t[44] │
│1.0 │
│-0.0 + 1.0 x[44]│
└ ┘ ∈ PowerCone{Float64}(0.6666666666666666)
┌ ┐
│0.0 + 1.0 t[45] │
│1.0 │
│-0.0 + 1.0 x[45]│
└ ┘ ∈ PowerCone{Float64}(0.6666666666666666)
┌ ┐
│0.0 + 1.0 t[46] │
│1.0 │
│-0.0 + 1.0 x[46]│
└ ┘ ∈ PowerCone{Float64}(0.6666666666666666)
┌ ┐
│0.0 + 1.0 t[47] │
│1.0 │
│-0.0 + 1.0 x[47]│
└ ┘ ∈ PowerCone{Float64}(0.6666666666666666)
┌ ┐
│0.0 + 1.0 t[48] │
│1.0 │
│-0.0 + 1.0 x[48]│
└ ┘ ∈ PowerCone{Float64}(0.6666666666666666)
┌ ┐
│0.0 + 1.0 t[49] │
│1.0 │
│-0.0 + 1.0 x[49]│
└ ┘ ∈ PowerCone{Float64}(0.6666666666666666)
┌ ┐
│0.0 + 1.0 t[50] │
│1.0 │
│-0.0 + 1.0 x[50]│
└ ┘ ∈ PowerCone{Float64}(0.6666666666666666)
------------------------------------------------------------------
COSMO v0.8.10 - A Quadratic Objective Conic Solver
Michael Garstka
University of Oxford, 2017 - 2022
------------------------------------------------------------------
Problem: x ∈ R^{155},
constraints: A ∈ R^{306x155} (634 nnz),
matrix size to factor: 461x461,
Floating-point precision: Float64
Sets: Nonnegatives of dim: 150
ZeroSet of dim: 6
PowerCone of dim: 3
PowerCone of dim: 3
PowerCone of dim: 3
... and 47 more
Settings: ϵ_abs = 1.0e-05, ϵ_rel = 1.0e-05,
ϵ_prim_inf = 1.0e-04, ϵ_dual_inf = 1.0e-04,
ρ = 0.1, σ = 1e-06, α = 1.6,
max_iter = 5000,
scaling iter = 10 (on),
check termination every 25 iter,
check infeasibility every 40 iter,
KKT system solver: QDLDL
Acc: Anderson Type2{QRDecomp},
Memory size = 15, RestartedMemory,
Safeguarded: true, tol: 2.0
Setup Time: 5.94ms
Iter: Objective: Primal Res: Dual Res: Rho:
1 -7.1941e-02 6.0310e-01 5.9631e-02 1.0000e-01
25 -5.9418e-02 2.6494e-04 5.4811e-05 1.0000e-01
50 -5.9411e-02 2.3555e-06 5.8473e-08 1.0000e-01
------------------------------------------------------------------
>>> Results
Status: Solved
Iterations: 50
Optimal objective: -0.05941
Runtime: 0.106s (105.64ms)Let's look at the expected return and the total transaction cost:
x_opt = JuMP.value.(x);
y_opt = JuMP.value.(y);
s_opt = JuMP.value.(s);
t_opt = JuMP.value.(t);
expected_return = dot(μ, x_opt)0.08425056098445659expected_risk = dot(y_opt, y_opt)0.0002708727203788806transaction_cost = a * sum(s_opt) + b * sum( t_opt)0.020409989166347835References
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