Conic quadratic optimization

Conic quadratic optimization is a problem of the form

$\begin{array}{lccr} \displaystyle{} \mbox{minimize}&\displaystyle{} c^{T} x &\displaystyle{} &\displaystyle{}\\ \displaystyle{} \mbox{subject to}&\displaystyle{} A x &\displaystyle{} = &\displaystyle{} b, \\ \displaystyle{} &\displaystyle{} x \in{} K &\displaystyle{} &\displaystyle{}\\ \end{array}$

where K is convex quadratic cone. An alternative name for conic quadratic optimization is second order cone programming.