Piecewise-convex maximization problems: Algorithm and computational experiments

A function F : R-n --> R is called a piecewise convex function if it can be decomposed into F(x) = min {f (j)(x) | j is an element of M}, where f(j) : R-n --> R is convex for all j is an element of M = {1 2..,m}. In this article, we provide an algorithm for solving max F( x) subject to x D, 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.