Second-order cone programming: Difference between revisions

Revision as of 09:19, 1 August 2025

Revision as of 09:22, 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]]. HereThe nomenclature here can be confusing; here <math>M\succcurlyeq 0 </math> means <math>M </math> is a semidefinite matrix: that is to say

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

which is not a linear inequality in the conventional sense.

Similarly, we also have,