Piecewise-Convex Maximization Problems: Algorithm and Computational Experiments

A function F : Rⁿ R is called a piecewise convex function if it can be decomposed into F(x)=min{f _j(x) j M}, where f _j :Rⁿ R is convex for all j M={1,2...,m}. In this article, we provide an algorithm for solving F(x) subject to xD, which is based on global optimality conditions. We report first computational experiments on small examples and open up some issues to improve the checking of optimality conditions.