Abstract

Necessary and sufficient optimality conditions are given for the following problem: \[ \min(g\circ F)(x),\text{ s.t. }x\in C, f_i(x)\leq 0, i=1,2, \dots, m \] where \(F:\mathbb{R}^n\to \mathbb{R}^m\) is a continuous nonsmooth map, \(g:\mathbb{R}^m \to\mathbb{R}\) is a convex function, \(C\subset R^n\) is a closed convex set, and \(f_i:\mathbb{R}^n \to\mathbb{R}\) is continuous for each \(i\). This type of problems subsumes a large class of problems arising in applications.