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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 (Shen and Yu, IEEE Trans Signal Process 66(10):2616–2630, 2018) which finds stationary points of concave-convex sum-of-ratios problems. We further use elements of the algorithm proposed by Shen and Yu 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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On Low-Rank Convex-Convex Quadratic Fractional Programming

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  • 发表日期：

    2025年

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  • Ilya Krishtal,
  • Brendan Miller

摘要

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 (Shen and Yu, IEEE Trans Signal Process 66(10):2616–2630, 2018) which finds stationary points of concave-convex sum-of-ratios problems. We further use elements of the algorithm proposed by Shen and Yu and the classic Dinkelbach approach to ensure convergence. We show that our algorithm performs better than previous algorithms for low-rank problems.