Global optimization of nonlinear sum of ratios problem

摘要

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.