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Gabay, D. and Mercier, B. (1976) A Dual Algorithm for the Solution of Nonlinear Variational Problems via Finite Element Approximation. Computers & Mathematics with Applications, 2, 17-40.
https://doi.org/10.1016/0898-1221(76)90003-1

has been cited by the following article:

• TITLE: Convergence of Generalized Bregman Alternating Direction Method of Multipliers for Nonconvex Objective with Linear Constraints

  AUTHORS: Junping Yao, Mei Lu

  KEYWORDS: Generalized Bregman Alternating Direction Method of Multipliers, Nonconvex Optimization, Lipschitz-Like Convexity Condition, Kurdyka-Lojasiewicz Inequality

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.13 No.4, April 10, 2025

  ABSTRACT: In this paper, we investigate the convergence of the generalized Bregman alternating direction method of multipliers (ADMM) for solving nonconvex separable problems with linear constraints. This algorithm relaxes the requirement of global Lipschitz continuity of differentiable functions that is often seen in many researches, and it incorporates the acceleration technique of the proximal point algorithm (PPA). As a result, the scope of application of the algorithm is broadened and its performance is enhanced. Under the assumption that the augmented Lagrangian function satisfies the Kurdyka-Lojasiewicz inequality, we demonstrate that the iterative sequence generated by the algorithm converges to a critical point of its augmented Lagrangian function when the penalty parameter in the augmented Lagrangian function is sufficiently large. Finally, we analyze the convergence rate of the algorithm.