Attractive force search algorithm for piecewise convex maximization problems

We consider mathematical programming problems with the so-called piecewise convex objective functions. A solution method for this interesting and important class of nonconvex problems is presented. This method is based on Newton??s law of universal gravitation, multicriteria optimization and Helly??s theorem on convex bodies. Numerical experiments using well known classes of test problems on piecewise convex maximization, convex maximization as well as the maximum clique problem show the efficiency of the approach.