"Branch and Bound" and "Branch and Reduce" approaches for a class of D.C. Programs

In this Ph.D. thesis an important class of d.c. programs is studied from both a theoretical and an algorithmic point of view. This class of problems is computationally studied with a "branch and bound" and a "branch and reduce" approaches, pointing out the effectiveness of partitioning rules and of stack policies for managing the branches. In this light, the results appeared in the literature are extended and deepened on. This study can be virtually divided into three main steps

Solving linear multiplicative programs via branch-and-bound: a computational experience

In this paper, linear multiplicative programs are approached with a branch-and-bound scheme and a detailed computational study is provided. Several underestimation functions are analyzed and various partitioning criteria are presented. A particular class of linear multiplicative programs, useful to solve some applicative bilevel problems, is considered from a theoretical point of view to emphasize an efficient solution method. Detailed results of the computational study are provided to point out the performances provided by using various underestimation functions and partitioning criteria, thus improving some of the results of the current literature

A branch and reduce approach for solving a class of low rank d.c. programs

Various classes of d.c. programs have been studied in the recent literature due to their importance in applicative problems. In this paper we consider a branch and reduce approach for solving a class of d.c. problems. Seven partitioning rules are analyzed and some techniques aimed at improving the overall performance of the algorithm are proposed. The results of a computational experience are provided in order to point Out the performance effectiveness of the proposed techniques. (C) 2009 Elsevier B.V. All rights reserved