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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 semidefinite matrix). Similarly, we also have,
:<math>\lVert A_i x + b_i \rVert_2 \leq c_i^T x + d_i \Leftrightarrow
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