Solving min–max linear fractional programs based on image space branch-and-bound scheme

Abstract

Based on the image space branch-and-bound scheme, this paper presents a novel algorithm for globally solving the min–max linear fractional programs (MMLFP), which has many applications in management optimization, engineering optimization, economic investment and so on. For finding the global optimal solution of the MMLFP, by leading into new parameter, we firstly transform the MMLFP into an equivalent fractional problem (EFP). Next, by using convex hull and concave hull approximation of bilinear function, we construct the linear relaxation problem (LRP) for computing the lower bound of the global minimum value of the EFP in the image space branch-and-bound algorithm. By subsequently solving a series of linear relaxation problems and refining the initial image space rectangle, the proposed algorithm is globally convergent to the optimum solution of the EFP. In addition, we give the computational complexity analysis of the algorithm based on the exhaustive branching rule. Finally, computational comparisons show better computational performance of the algorithm.