# Semi-definite program

$LaTeX: \textstyle \min \{cx: S(x) \in P\},$ where $LaTeX: \mbox{P}$ is the class of positive semi-definite matrices, and $LaTeX: \textstyle \mbox{S}(x) = S_0 + \sum_{j} x(j)S_j ,$ where each $LaTeX: \textstyle \mbox{S}_j,$ for $LaTeX: \textstyle j = 0,\dots,n$ is a (given) symmetric matrix. This includes the linear program as a special case.