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运筹学学报 >

2025 , Vol. 29 >Issue 2: 80 - 94

DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2025.02.006

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非凸复合优化问题的黄金比率邻近交替线性化算法

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  • 1. 重庆工商大学数学与统计学院, 重庆 400067
龙宪军, E-mail: xianjunlong@ctbu.edu.cn

收稿日期: 2024-07-21

  网络出版日期: 2025-06-12

基金资助

重庆市自然科学基金(CSTB2024NSCQ-MSX1282);重庆市研究生导师团队建设项目(yds223010);重庆工商大学研究生创新型科研项目(yjscxx2025-269-238)

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运筹学学报编辑部, 2025, 版权所有，未经授权，不得转载。
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A golden ratio proximal alternating linearized algorithm for nonconvex composite optimization problems

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  • 1. School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China

Received date: 2024-07-21

  Online published: 2025-06-12

Copyright

, 2025, All rights reserved. Unauthorized reproduction is prohibited.
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摘要

本文考虑一类完全非凸的复合优化问题, 其目标函数由如下两部分组成: 关于全局变量不可分的连续可微非凸函数, 与两个关于独立变量的正常下半连续非凸函数。本文提出一种求解该问题的新型黄金比率邻近交替线性化极小化算法。在Kurdyka-Lojasiewicz (简记KL)性质假设下, 证明了由算法产生的迭代序列收敛到问题的稳定点。最后将新算法应用于求解稀疏信号恢复问题, 数值实验验证了新算法的有效性与优越性。

关键词： 非凸复合优化问题; 黄金比率邻近交替线性化算法; KL性质; 收敛性

本文引用格式

曾康, 龙宪军 . 非凸复合优化问题的黄金比率邻近交替线性化算法[J]. 运筹学学报, 2025 , 29(2) : 80 -94 . DOI: 10.15960/j.cnki.issn.1007-6093.2025.02.006

Abstract

In this paper, we consider a class of nonconvex composite optimization problems, whose objective function is the sum of a continuous differentiable bifunction of the entire variables, and two proper lower semi-continuous nonconvex function of their private variables. We propose a new golden ratio proximal alternating linearized algorithm to solve this problem. Under the assumption of Kurdyka-Lojasiewicz (in short: KL) property, we prove the iterative sequence generated by the algorithm converges to the critical point of the problem. Finally, numerical results on sparse signal recovery illustrate the efficiency and superiority of the proposed algorithm.

Key words： nonconvex composite optimization problem; golden ration proximal alternating linearized algorithm; KL property; convergence

参考文献

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