Inverse Quadratic Transform for Minimizing A Sum of Ratios

Abstract

A major challenge with the multi-ratio Fractional Program (FP) is that the existing methods for the maximization problem typically do not work for the minimization case. We propose a novel technique called inverse quadratic transform for the sum-of-ratios minimization problem. Its main idea is to reformulate the min-FP problem in a form amenable to efficient iterative optimization. Furthermore, this transform can be readily extended to a general cost-function-of-multiple-ratios minimization problem. We also give a Majorization-Minimization (MM) interpretation of the inverse quadratic transform, showing that all those desirable properties of MM can be carried over to the new technique. Moreover, we demonstrate the application of inverse quadratic transform in minimizing the Age-of-Information (AoI) of data networks.