A simplicial branch-and-bound algorithm conscious of special structures in concave minimization problems

Abstract

In this paper, we develop a simplicial branch-and-bound algorithm for generating globally optimal solutions to concave minimization problems with low rank nonconvex structures. We propose to remove all additional constraints imposed on the usual linear programming relaxed problem. Therefore, in each bounding operation, we solve a linear programming problem whose constraints are exactly the same as the target problem. Although the lower bound worsens as a natural consequence, we offset this weakness by using an inexpensive bound tightening procedure based on Lagrangian relaxation. After giving a proof of the convergence, we report a numerical comparison with existing algorithms.

Optimization Method for Globally Solving a Kind of Multiplicative Problems with Coefficients

“…Large number of solution algorithms for linear multiplicative problems can be classified as follows [Refs. [6][7][8][9][10][11][12][13][14]: parameterization-based methods, outer-approximation methods, a vertex enumeration method, a method based on image space analysis, a primal and dual simplex method, heuristic methods, and a cutting plane method in outcome space.…”