A '''Second order cone program''' ('''SOCP''') is a [[convex optimization]] problem of the form
minimize <math>\ f^T x \ </math> subject to
<math>\lVert A_i x + b_i \rVert_2 \leq c_i^T x + d_i</math>,\quad <math>i\in\{ = 1,\dots,m\}</math>
<math>Fx = g \ </math>
where <math>x</math> is the optimizationproblem variable,parameters are <math>f \in \mathbb{R}^n, \ A_i \in \mathbb{R}^{{n_i}\times n}, \ b_i \in \mathbb{R}^{n_I}, \ c_i \in \mathbb{R}^n, \ d_i \in \mathbb{R}, \ F \in \mathbb{R}^{p\times n}</math>, and <math>Fg \in \mathbb{R}^{p\times</math>. nHere <math>x\in\mathbb{R}^n</math> is the optimization variable. When <math>A_i = 0</math> for <math>i\in\{ = 1,\dots,m\}</math>, the SOCP reduces to a [[linear program]]. When <math>c_i = 0 </math> for <math>i\in\{ = 1,\dots,m\}</math>, the SOCP is equivalent to a [[Quadratically constrained quadratic program]].
