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.