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:

“Will women find themselves in the same position they have always been? Or do we see liberation as solving the conditions of women in our society?... If we continue to shy away from this problem we will not be able to solve it after independence. But if we can say that our first priority is the emancipation of women, we will become free as members of an oppressed community.”
—Ruth Mompati (b. 1925)