picos.expressions.cone_soc¶

Outline¶

The second order cone.

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

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

$\mathcal{Q}^n = \left\{ x \in \mathbb{R}^n ~\middle|~ x_1 \geq \sqrt{\sum_{i = 2}^n x_i^2} \right\}.$

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