Second-order cone programming: Difference between revisions

Revision as of 09:11, 1 August 2025

Revision as of 09:17, 1 August 2025

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:<math>||x||\leq t \Leftrightarrow \begin{bmatrix} tI & x \\ x^T & t \end{bmatrix} \succcurlyeq 0,</math>

i.e., a second-order cone constraint is equivalent to a [[linear matrix inequality]] (Here <math>M\succcurlyeq 0 </math> means <math>M </math> is a semidefinite matrix).: Similarly,that weis alsoto have,say

:<math>\mathbf{x}^\mathsf{T} M\mathbf{x} \geq 0 \text{ for all } \mathbf{x} \in \mathbb{R}^n</math>.

Similarly, we also have,

:<math>\lVert A_i x + b_i \rVert_2 \leq c_i^T x + d_i \Leftrightarrow