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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