A Relaxed Alternating Direction Method Of Multipliers For Separable Nonconvex Minimization Problems

Jing Zhao (), Chenzheng Guo () and Xiaolong Qin ()
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Jing Zhao: Civil Aviation University of China
Chenzheng Guo: Xidian University
Xiaolong Qin: Hangzhou Normal University

Journal of Optimization Theory and Applications, 2025, vol. 207, issue 1, No 17, 29 pages

Abstract: Abstract The alternating direction method of multipliers (ADMM) is popular and powerful in computing the solutions of various composite minimization problems with constraints. In this paper, we propose a relaxed ADMM with a general dual step-size, which includes the classic ADMM in the algorithm framework, for minimizing separable nonconvex functions with linear constraints. Under some assumptions on the penalty parameter and the objective function, the convergence of the proposed algorithm is obtained based on the Kurdyka–Łojasiewicz property. Moreover, we report some preliminary numerical results on involving matrix decomposition problem to demonstrate the feasibility and effectiveness of the proposed method.

Keywords: Alternating direction method of multipliers; Kurdyka–Łojasiewicz property; Linear constraints; Nonconvex optimization; 65K15; 90C26; 90C30 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02778-2

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