A Global Optimization Method for the Nonlinear Sum of Ratios Problem

This article presents global optimization algorithm for globally solving the nonlinear sum of ratios problem (NRS) on nonconvex feasible region. Two folds are presented. Firstly, a problem (P1) is derived which is equivalent to problem (NRS). Second, by utilizing the parametric linearization relaxation method, initial non-convex nonlinear problem (NRS) is reduce to a sequence of linear programming problems through the successive refinement of a linear relaxation of feasible region and of the objective function. 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. A numerical example is given to illustrate the feasibility of the present algorithm.