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.

在本文中，我们研究了受凸和非凸二次约束的二次函数的非凸最小 - 最大分数问题。首先，通过使用 Dinkelbach 型方法，我们将分数问题转化为单变量非线性方程。为了评估这个方程，我们需要解决一个非凸二次约束二次规划 (QCQP) 问题。为了解决这个问题，我们提出了一种新方法。在所提出的方法中，首先，通过使用非凸QCQP问题的非凸约束的松弛和凸化，获得最优值的上限和下限。通过使用这些边界，我们构建了一个具有两个约束的参数 QCQP 问题。然后，通过解决新问题，为下一次迭代更新该问题的参数。我们表明，新问题的解序列收敛于非凸 QCQP 问题的全局最优解。给出的数值结果表明了该方法的适用性。