On Low-Rank Convex-Convex Quadratic Fractional Programming

Ilya Krishtal; Brendan Miller

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arXiv · 2301.11269

On Low-Rank Convex-Convex Quadratic Fractional Programming

Ilya Krishtal·Brendan Miller

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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.

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Ilya Krishtal, Brendan Miller. 2023-01-26. On Low-Rank Convex-Convex Quadratic Fractional Programming. https://arxiv.org/abs/2301.11269

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