A deterministic global optimization algorithm

In this paper, we consider a deterministic global optimization algorithm for solving a general linear sum of ratios (LFP). First, an equivalent optimization problem (LFP1) of LFP is derived by exploiting the characteristics of the constraints of LFP. By a new linearizing method the linearization relaxation function of the objective function of LFP1 is derived, then the linear relaxation programming (RLP) of LFP1 is constructed and the proposed branch and bound algorithm is convergent to the global minimum through the successive refinement of the linear relaxation of the feasible region of the objection function and the solutions of a series of RLP. And finally the numerical experiments are given to illustrate the feasibility of the proposed algorithm.