A Single-loop Proximal Subgradient Algorithm for A Class Structured Fractional Programs

In this paper, we investigate a class of nonconvex and nonsmooth fractional programming problems, where the numerator composed of two parts: a convex, nonsmooth function and a differentiable, nonconvex function, and the denominator consists of a convex, nonsmooth function composed of a linear operat...

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Bibliographic Details
Published in:Journal of scientific computing Vol. 104; no. 3; p. 75
Main Authors: Han, Deren, Tao, Min, Xia, Zihao
Format: Journal Article
Language:English
Published: New York Springer US 01.09.2025
Springer Nature B.V
Subjects:
Algorithms
Computational Mathematics and Numerical Analysis
Decoupling
Linear operators
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematical programming
Mathematics
Mathematics and Statistics
Optimization
Recovery
Signal reconstruction
Theoretical
Decoupling
Fractional programming
Single-loop
Convergence analysis
ISSN:0885-7474, 1573-7691
Online Access:Get full text
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Summary:In this paper, we investigate a class of nonconvex and nonsmooth fractional programming problems, where the numerator composed of two parts: a convex, nonsmooth function and a differentiable, nonconvex function, and the denominator consists of a convex, nonsmooth function composed of a linear operator. These structured fractional programming problems have broad applications, including CT reconstruction, sparse signal recovery, the single-period optimal portfolio selection problem and standard Sharpe ratio minimization problem. We develop a single-loop proximal subgradient algorithm that alleviates computational complexity by decoupling the evaluation of the linear operator from the nonsmooth component. We prove the global convergence of the proposed single-loop algorithm to an exact lifted stationary point under the Kurdyka-Łojasiewicz assumption. Additionally, we present a practical variant incorporating a nonmonotone line search to improve computational efficiency. Finally, through extensive numerical simulations, we showcase the superiority of the proposed approach over the existing state-of-the-art methods for three applications: L 1 / S κ sparse signal recovery, limited-angle CT reconstruction, and optimal portfolio selection.
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ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-025-02987-x