Convex Optimization - Convex Optimization Problem

Convex Optimization Problem

An optimization problem (also referred to as a mathematical programming problem or minimization problem) of finding some such that

where is the feasible set and is the objective, is called convex if is a closed convex set and is convex on . Alternatively, an optimization problem on the form

$\begin{align} &\operatorname{minimize}& & f(x) \\ &\operatorname{subject\;to} & &g_i(x) \leq 0, \quad i = 1,\dots,m \end{align}$

is called convex if the functions are convex.

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