Optimizing generalized linear fractional program using the image space branch-reduction-bound scheme

This paper addresses solving the generalized linear fractional program problem. For this purpose, we first convert the original problem into an equivalent problem by introducing some new variables and equivalent variation. Next, by using the two-part approximation and bilinear relaxation, we construct the linear relaxation of the objective function and the constraint function, respectively. Based on the characteristics of the objective functions of the equivalence problem and the relaxation problem and the branch-and-bound structure of the algorithm, we construct some image space region reduction techniques to enhance the convergence speed of the algorithm. By combining the linear relaxation program problem and the image space region reduction techniques, we construct an image space branch-reduction-bound algorithm, prove its global convergence, and estimate its maximum number of iterations in the worst case by analysing the complexity. Finally, numerical results indicate high computational efficiency of the algorithm.