Implements SecondOrderCone.


class picos.expressions.cone_soc.SecondOrderCone(dim=None)[source]

Bases: picos.expressions.cone.Cone

The second order cone.

Also known as the quadratic, 2-norm, Lorentz, or ice cream cone.

For n \in \mathbb{Z}_{\geq 2}, represents the convex cone

\mathcal{Q}^n = \left\{
    x \in \mathbb{R}^n
    x_1 \geq \sqrt{\sum_{i = 2}^n x_i^2}

Dual cone

The second order cone as defined above is self-dual.


Construct a second order cone.

property dual_cone

Implement cone.Cone.dual_cone.