cones

class Cone

Bases: object

A generic class for cones.

class Exp

Bases: Cone

The primal exponential cone.

\[\mathcal{K}_\text{exp} = \{{x=(x_0,x_1,x_2) \text{ s.t. } x_0 \geq x_1\exp(x_2/x_1), \:\: x_0,x_1\geq 0\}}\]

property dual

The dual exponential cone.

class Pow(dim: int, alpha: float)

Bases: Cone

The primal power cone.

\[\mathcal{P}_{{\alpha,1-\alpha}}=\{{x=(x_0,x_1,\bar{{x}}) \text{ s.t. } \|\bar{{x}}\|_2^2 \leq x_0^\alpha x_1^{{1-\alpha}}\}}\]

Parameters:

• dim (int) – dimension of the cone (>= 3)

• alpha (float) – Power-cone exponent, must be between 0 and 1.

property dual

The dual power cone.

class Product(list_K)

Bases: Cone

Direct product of cones.

class Quad(dim: int = 1)

Bases: Cone

The quadratic cone.

\[\mathcal{Q}=\{{x=(x_0,\bar{{x}}) \text{ s.t. } \|\bar{{x}}\|_2 \leq x_0\}}\]

Parameters:

dim (int, optional) – dimension of the cone, by default 1

class RQuad(dim: int = 1)

Bases: Cone

The rotated quadratic cone.

\[\]

mathcal{Q}_r={{x=(x_0,x_1,bar{{x}}) text{ s.t. } |bar{{x}}|_2^2 leq 2x_0x_1}}

Parameters:

dim (int, optional) – dimension of the cone, by default 1

class SDP(dim: int)

Bases: Cone

The cone of positive semi-definite matrices.

\[\mathcal{{S}}=\{{\boldsymbol{{X}}\in \mathbb{R}^{n imes n} \text{ s.t. } \boldsymbol{{X}}=\boldsymbol{{X}}^T \text{ and } \boldsymbol{{X}}\succeq 0\}}\]

Parameters:

dim (int) – Dimension \(n\) of the PSD \(n\times n\) matrix