cones#
- class fenics_optim.cones.Cone#
Bases:
objectA generic class for cones.
- class fenics_optim.cones.Exp(dim: int)#
Bases:
fenics_optim.cones.ConeThe primal exponential cone.
- class fenics_optim.cones.Pow(dim: int, alpha: float)#
Bases:
fenics_optim.cones.ConeThe 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.ConeDirect product of cones.
- class fenics_optim.cones.Quad(dim: int = 1)#
Bases:
fenics_optim.cones.ConeThe 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.ConeThe 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.ConeThe 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