On the complex fractional quadratic optimization with a quadratic constraint

In this paper, we study the problem of minimizing the ratio of two complex indefinite quadratic functions subject to a strictly convex quadratic constraint. First, using the known method due to Dinkelbach, we reformulate the fractional problem as a univariate equation. To find the root of the univariate equation, the generalized Newton method is utilized that requires solving a nonconvex quadratic optimization problem at each iteration. To solve these nonconvex quadratic problems, we present an efficient algorithm by a diagonalization scheme that requires solving a univariate minimization problem at each iteration. Moreover, for the homogeneous case, it requires solving a simple linear optimization problem. Our preliminary numerical experiments on several randomly generated test problems show that, the new approach is much faster in finding the global optimal solution than the known semidefinite relaxation approach, especially when solving large scale problems. © 2016, Operational Research Society of India.