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Operations Research Transactions >

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

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

Research Article

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

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

Cite this article

Kang ZENG, Xianjun LONG . A golden ratio proximal alternating linearized algorithm for nonconvex composite optimization problems[J]. Operations Research Transactions, 2025 , 29(2) : 80 -94 . DOI: 10.15960/j.cnki.issn.1007-6093.2025.02.006

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