On Low-Rank Convex-Convex Quadratic Fractional Programming

TL;DR

This paper introduces an efficient algorithm for solving a class of fractional programming problems with low-rank quadratic objectives, combining the Shen-Yu Quadratic Transform and Dinkelbach approach for improved convergence.

Contribution

The paper proposes a novel algorithm specifically designed for low-rank convex-convex quadratic fractional programming problems, enhancing performance over existing methods.

Findings

Algorithm outperforms previous methods on low-rank problems

Ensures convergence through combined Shen-Yu transform and Dinkelbach approach

Effective for convex constraints in quadratic fractional programming

Abstract

We present an efficient algorithm for solving fractional programming problems whose objective functions are the ratio of a low-rank quadratic to a positive definite quadratic with convex constraints. The proposed algorithm for these convex-convex problems is based on the Shen-Yu Quadratic Transform which finds stationary points of concave-convex sum-of-ratios problems. We further use elements of the algorithm proposed in [arXiv:1802.10192] and the classic Dinkelbach approach to ensure convergence. We show that our algorithm performs better than previous algorithms for low-rank problems.