Convex program

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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.

Here are some key properties of a convex program:

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