Supported Cone Types
Clarabel natively supports optimization problems with conic constraints defined on the following cones:
| Cone Type | Constructor | Definition |
|---|---|---|
| Zero cone | ZeroConeT(n) | $\{ 0 \}^{n}$ |
| Nonnegative Orthant | NonnegativeConeT(n) | $\{ x \in \mathbb{R}^{n} : x_i \ge 0, \forall i=1,\dots,\mathrm{n} \}$ |
| Second-Order Cone | SecondOrderConeT(n) | $\{ (t,x) \in \mathbb{R}^{n} : ||x||_2 \leq t \}$ |
| Exponential Cone | ExponentialConeT() | $\{(x, y, z) : y > 0,~~ ye^{x/y} ≤ z \}$ |
| Power Cone | PowerConeT(a) | $\{(x, y, z) : x^a y^{(1-a)} \geq |z|,~ (x,y) \geq 0 \}$ with $a \in (0,1)$ |
| Generalized Power Cone | GenPowerConeT(a,n) | $\{(x, y) \in \mathbb{R}^{len(a)} \times \mathbb{R}^{n} : \prod\limits_{a_i \in a} x_i^{a_i} \geq ||y||_2,~ x \ge 0 \}$ with $a_i \in (0,1)$ and $\sum a_i = 1$ |
| Positive Semidefinite Cone (triangular part) | PSDTriangleConeT(n) | Upper triangular part of the positive semidefinite cone $\mathbb{S}^{n}_+$. The elements $x$ of this cone represent the columnwise stacking of the upper triangular part of a positive semidefinite matrix $X \in \mathbb{S}^{n}_+$, so that $x \in \mathbb{R}^d$ with $d = {n(n+1)}/{2}.$ |