Semidefinite programming

A semidefinite program has the form:

$$\text{minimize } c^T x$$ $$\begin{matrix}\text{subject to} & x_1 F_1 + \dots + x_n F_n + G \le 0 \\ & Ax = b\end{matrix}$$

where $$F_i, G$$ are symmetric matrices and $$\le $$ refers to negative definiteness of a matrix.

Semidefinite program is a powerful form as a large set of inequality-constrained (convex) optimization problems can be converted to a semidefinite program.