Piecewise-Convex Maximization Problems

Abstract

A function F:Rⁿ→ R is called a piecewise convex function if it can be decomposed into $F(x) = \min \left\{ {\user1{f}j(x){\mathbf{|}}j \in M} \right\}$, where f _j:Rⁿ→ R is convex for all j∈M={1,2...,m}. We consider $\user1{f}j:R^n \to R$ subject to x∈D. It generalizes the well-known convex maximization problem. We briefly review global optimality conditions for convex maximization problems and carry one of them to the piecewise-convex case. Our conditions are all written in primal space so that we are able to proposea preliminary algorithm to check them.