A Deterministic Algorithm for Min-max and Max-min Linear Fractional Programming Problems

In this paper, a deterministic global optimization algorithm is proposed for solving min-max and max-min linear fractional programming problem (P) which have broad applications in engineering, management science, nonlinear system, economics and so on. By utilizing equivalent problem (Q) of the (P) and two-phase linear relaxation technique, the relaxation linear programming (RLP) about the (P) is established. The proposed algorithm is convergent to the global minimum of (P) through the successive refinement of the feasible region and solutions of a series of RLP. And finally the numerical examples are given to illustrate the feasibility of the presented algorithm.