Conic set
1 Cone
A non-empty set S is called a cone, if:
\forall x \in S, \; \theta \ge 0 \;\; \rightarrow \;\; \theta x \in S
2 Convex cone
The set S is called a convex cone, if:
\forall x_1, x_2 \in S, \; \theta_1, \theta_2 \ge 0 \;\; \rightarrow \;\; \theta_1 x_1 + \theta_2 x_2 \in S
Example
- \mathbb{R}^n
- Affine sets, containing 0
- Ray
- \mathbf{S}^n_+ - the set of symmetric positive semi-definite matrices