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Jia, Z., Gao, X., Cai, X. and Han, D. (2021) The Convergence Rate Analysis of the Symmetric ADMM for the Nonconvex Separable Optimization Problems. Journal of Industrial & Management Optimization, 17, 1943-1971.
https://doi.org/10.3934/jimo.2020053

has been cited by the following article:

• TITLE: A Symmetric Alternating Direction Method of Multipliers with Two Different Relaxation Factors for Solving Non-Separable Nonconvex Minimization Problems

  AUTHORS: Mei Lu, Zidan Wang

  KEYWORDS: Symmetric Alternating Direction Method of Multipliers, Non-Separable Structure, Nonconvex Optimization, Kurdyka-Łojasiewicz Inequality

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.14 No.4, April 28, 2026

  ABSTRACT: This paper proposes a symmetric alternating direction method of multipliers with two different relaxation factors for solving nonconvex optimization problems with linear constraints and a non-separable structure. Although many studies have proposed variants of symmetric ADMM with a single relaxation factor, incorporating techniques such as Bregman distances, inertial terms, regularization terms, or linearization, the most basic form of symmetric ADMM with two different relaxation factors for solving non-separable problems has not yet been resolved. The introduction of two different relaxation factors in this method yields a broader range of parameters, making it applicable to more practical problems, and also provides a fundamental theoretical basis for accelerating the algorithm with other techniques. Based on the Kurdyka-Łojasiewicz property, we establish the convergence of the sequences generated by the proposed algorithm and analyze its convergence rate.