A multi-parameter parallel ADMM for multi-block linearly constrained separable convex optimization

• Published in: Applied numerical mathematics Vol. 171; pp. 369 - 388
• Main Authors: Shen, Yuan, Gao, Qianming, Yin, Xue
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.01.2022
• Subjects: Alternating direction method of multipliers; Convex optimization; Multi-block; Parallel computing; Proximal point algorithm; Multi-block; Alternating direction method of multipliers; Parallel computing; Proximal point algorithm; Convex optimization
• ISSN: 0168-9274; 1873-5460
• DOI: 10.1016/j.apnum.2021.09.011

The alternating direction method of multipliers (ADMM) has been proved to be effective for solving two-block convex minimization model subject to linear constraints. However, the convergence of multiple-block convex minimization model with linear constraints may not be guaranteed without additional assumptions. Recently, some parallel multi-block ADMM algorithms which solve the subproblems in a parallel way have been proposed. This paper is a further study on this method with the purpose of improving the parallel multi-block ADMM algorithm by introducing more parameters. We propose two multi-parameter parallel ADMM algorithms with proximal point terms attached to all subproblems. Comparing with some popular parallel ADMM-based algorithms, the parameter conditions of the new algorithms are relaxed. Experiments on both real and synthetic problems are conducted to justify the effectiveness of the proposed algorithms compared to several efficient ADMM-based algorithms for multi-block problems.