# Convex program

The mathematical program $LaTeX: \min \{f(x) : x \in X \}$ is convex if the objective function $LaTeX: f$ is convex, and the feasible region $LaTeX: X$ is a convex set. In particular, the mathematical program $LaTeX: \min \{f(x) : g(x) \le 0, \; h(x) = 0 \}$ is convex if $LaTeX: g$ is convex, and $LaTeX: h$ is affine. See the supplement, Convex Cones, Sets, and Functions.