Motivation and Overview

Abstract

We will be concerned with optimization problems of the general form

$$\min \{ f\left( x \right)|g_i \left( x \right) \leqslant 0\left( {i = 1, \ldots ,m} \right),x \in X\} $$

(P)

where X is a closed convex set in R ⁿ, f : Ω→ R and g _i : Ω→R, i= 1,…,m are functions defined on some set Ω in R ⁿ containing X. Denoting the feasible set by S:

$$S = \{ x \in X|g_i \left( x \right) \leqslant 0,i = 1, \ldots ,m\}$$

we can also write the problem as

$$\min \{ f(x)\left| {x \in S\} .} \right.$$