Solving sum of quadratic ratios fractional programs via monotonic function

In this paper, a branch-reduce-bound algorithm is proposed for globally solving a sum of quadratic ratios fractional programming with nonconvex quadratic constraints. Due to its intrinsic difficulty, less work has been devoted to globally solving this problem. The proposed algorithm is based on reformulating the problem as a monotonic optimization problem, and it turns out that the optimal solution which is provided by the algorithm is adequately guaranteed to be feasible and to be close to the actual optimal solution. Convergence of the algorithm is shown and the numerical experiments are given to show the feasibility of the proposed algorithm.