A hybrid method for solving non-convex min–max quadratic fractional problems under quadratic constraints

Abstract

In this paper, we study a non-convex min–max fractional problem of quadratic functions subject to convex and non-convex quadratic constraints. First, by using the Dinkelbach-type method, we transform the fractional problem into a univariate nonlinear equation. To evaluate this equation, we need to solve a non-convex quadratically constrained quadratic programming (QCQP) problem. To solve this problem, we propose a new method. In the proposed method, first, by using relaxation and convexification of non-convex constraints of non-convex QCQP problem, an upper bound and a lower bound of the optimal value is obtained. By using these bounds, we construct a parametric QCQP problem with two constraints. Then, by solution of the new problem, the parameters of this problem are updated for the next iteration. We show that the sequence of solutions of new problems is convergent to a global optimal solution of the non-convex QCQP problem. Numerical results are given to show the applicability of the proposed method.