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.

Read more about this topic:  Convex Optimization

Famous quotes containing the word problem:

    “In the nineteenth century the problem was that God is dead; in the twentieth century the problem is that man is dead.”
    —Erich Fromm (1900–1980)