Different strategies for solving bilinear integer non-linear programming problems with convex transformations

Abstract

In the present paper, some strategies for transforming integer bilinear functions into convex form are presented. Bilinear functions are non-convex and for such functions, no straightforward methods for finding the optimal solution exist. What makes the case in this paper especially interesting is the fact that the variables appearing in the bilinear function are all integers. The transformations are followed by an example and a comparison of the strategies applied to an originally non-convex mixed integer non-linear programming (MINLP) problem, the trim-loss problem. The example is based on trim-optimization problems encountered at a Finnish paper converting mill.