On reducibility of ADMM based on degenerate proximal point analysis

IF 2.4 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics Pub Date : 2026-10-01 Epub Date: 2026-02-27 DOI:10.1016/j.cam.2026.117531

Feng Xue

引用次数: 0

Abstract

We discuss the possibility of reducing the alternating direction method of multipliers (ADMM) to a simple resolvent form, based on a degenerate proximal point algorithm (PPA). In particular, we reformulate ADMM as a standard PPA without correction step, where the variable metric helps to identify and remove the redundant variables. This approach can be a general routine for the degeneracy reduction of any splitting algorithms.

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基于退化近端点分析的ADMM可约性研究

我们讨论了在退化近端算法（PPA）的基础上，将乘法器的交替方向法（ADMM）简化为一种简单的解算形式的可能性。特别是，我们将ADMM重新制定为没有校正步骤的标准PPA，其中可变度量有助于识别和删除冗余变量。这种方法可以作为降低任何分裂算法的退化的通用例程。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Computational and Applied Mathematics 数学-应用数学

CiteScore

5.40

自引率

4.20%

发文量

437

审稿时长

3.0 months

期刊介绍： The Journal of Computational and Applied Mathematics publishes original papers of high scientific value in all areas of computational and applied mathematics. The main interest of the Journal is in papers that describe and analyze new computational techniques for solving scientific or engineering problems. Also the improved analysis, including the effectiveness and applicability, of existing methods and algorithms is of importance. The computational efficiency (e.g. the convergence, stability, accuracy, ...) should be proved and illustrated by nontrivial numerical examples. Papers describing only variants of existing methods, without adding significant new computational properties are not of interest. The audience consists of: applied mathematicians, numerical analysts, computational scientists and engineers.