A novel convex relaxation-strategy-based algorithm for solving linear multiplicative problems

Abstract

Linear multiplicative programming (LMP) problems have many applications, although their solving can be difficult. To solve LMPs, we propose a convex approximation approach with a standard partition in intervals. First, a novel convex relaxation strategy is designed, which is used to obtain a convex relaxation problem, and provides a lower bound for LMPs. Then, through solving a sequence of convex relaxation programming problems, we can obtain an approximate optimal solution of LMPs. The main calculation of the algorithm focuses on solving these convex programming problems, which can be completed by a convex optimization software. Furthermore, the convergence and the complexity of the algorithm are discussed theoretically. Finally, numerical experiments show the effectiveness of the designed algorithm in terms of running time and the number of iterations.