cones#

class fenics_optim.cones.Cone#

Bases: object

A generic class for cones.

class fenics_optim.cones.Exp(dim: int)#

Bases: fenics_optim.cones.Cone

The primal exponential cone.

class fenics_optim.cones.Pow(dim: int, alpha: float)#

Bases: fenics_optim.cones.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) – [description]

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

class fenics_optim.cones.Product(list_K)#

Bases: fenics_optim.cones.Cone

Direct product of cones.

class fenics_optim.cones.Quad(dim: int = 1)#

Bases: fenics_optim.cones.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 fenics_optim.cones.RQuad(dim: int = 1)#

Bases: fenics_optim.cones.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 fenics_optim.cones.SDP(dim: int)#

Bases: fenics_optim.cones.Cone

The cone of positive semi-definite matrices.

\(\mathcal{{S}}=\{{\boldsymbol{{X}} \text{ s.t. } \boldsymbol{{X}}=\boldsymbol{{X}}^T \text{ and } \boldsymbol{{X}}\succeq 0\}}\)

Parameters

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