Global optimization of nonlinear sum of ratios problem

• Published in: Applied mathematics and computation Vol. 158; no. 2; pp. 319 - 330
• Main Authors: Wang, Yan-Jun, Zhang, Ke-Cun
• Format: Journal Article
• Language: English
• Published: New York, NY Elsevier Inc 05.11.2004; Elsevier
• Subjects: Branch and bound; Calculus of variations and optimal control; Exact sciences and technology; Global optimization; Mathematical analysis; Mathematics; Nonlinear sum of ratios; Numerical analysis; Numerical analysis. Scientific computation; Numerical methods in mathematical programming, optimization and calculus of variations; Sciences and techniques of general use; Branch and bound; Global optimization; Nonlinear sum of ratios; Lower bound; Numerical analysis; Algorithm performance; Applied mathematics; Optimization method; Linear programming; Nonlinear problems; Algorithm; Mathematical programming
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2003.08.113

This article presents a branch and bound algorithm for globally solving the nonlinear sum of ratios problem ( P) on nonconvex feasible region. First a problem ( Q) is derived which is equivalent to problem ( P). In the algorithm, lower bounds are derived by solving a sequence of linear relaxation programming problems, which is based on the construction of the linear lower bounding functions for the objective function and the constraint functions of the problem ( Q) over the feasible region. The proposed branch and bound algorithm is convergent to the global minimum through the successive refinement of the solutions of a series of linear programming problems. The numerical experiment is reported to show the feasibility and effectiveness of the proposed algorithm.