Sequential inertial linear ADMM algorithm for nonconvex and nonsmooth multiblock problems with nonseparable structure

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-05-08 DOI:10.1186/s13660-024-03141-1

Zhonghui Xue, Kaiyuan Yang, Qianfeng Ma, Yazheng Dang

{"title":"Sequential inertial linear ADMM algorithm for nonconvex and nonsmooth multiblock problems with nonseparable structure","authors":"Zhonghui Xue, Kaiyuan Yang, Qianfeng Ma, Yazheng Dang","doi":"10.1186/s13660-024-03141-1","DOIUrl":null,"url":null,"abstract":"The alternating direction method of multipliers (ADMM) has been widely used to solve linear constrained problems in signal processing, matrix decomposition, machine learning, and many other fields. This paper introduces two linearized ADMM algorithms, namely sequential partial linear inertial ADMM (SPLI-ADMM) and sequential complete linear inertial ADMM (SCLI-ADMM), which integrate linearized ADMM approach with inertial technique in the full nonconvex framework with nonseparable structure. Iterative schemes are formulated using either partial or full linearization while also incorporating the sequential gradient of the composite term in each subproblem’s update. This adaptation ensures that each iteration utilizes the latest information to improve the efficiency of the algorithms. Under some mild conditions, we prove that the sequences generated by two proposed algorithms converge to the critical points of the problem with the help of KŁ property. Finally, some numerical results are reported to show the effectiveness of the proposed algorithms.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1186/s13660-024-03141-1","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}

引用次数: 0

Abstract

The alternating direction method of multipliers (ADMM) has been widely used to solve linear constrained problems in signal processing, matrix decomposition, machine learning, and many other fields. This paper introduces two linearized ADMM algorithms, namely sequential partial linear inertial ADMM (SPLI-ADMM) and sequential complete linear inertial ADMM (SCLI-ADMM), which integrate linearized ADMM approach with inertial technique in the full nonconvex framework with nonseparable structure. Iterative schemes are formulated using either partial or full linearization while also incorporating the sequential gradient of the composite term in each subproblem’s update. This adaptation ensures that each iteration utilizes the latest information to improve the efficiency of the algorithms. Under some mild conditions, we prove that the sequences generated by two proposed algorithms converge to the critical points of the problem with the help of KŁ property. Finally, some numerical results are reported to show the effectiveness of the proposed algorithms.

查看原文本刊更多论文

针对具有不可分割结构的非凸和非光滑多块问题的序列惯性线性 ADMM 算法

交替方向乘法（ADMM）已被广泛用于解决信号处理、矩阵分解、机器学习等诸多领域的线性约束问题。本文介绍了两种线性化 ADMM 算法，即顺序部分线性惯性 ADMM (SPLI-ADMM) 和顺序完全线性惯性 ADMM (SCLI-ADMM)。迭代方案采用部分线性化或完全线性化，同时在每个子问题的更新中纳入复合项的连续梯度。这种调整确保每次迭代都能利用最新信息，从而提高算法的效率。在一些温和的条件下，我们证明了在 KŁ 属性的帮助下，两种拟议算法生成的序列收敛于问题的临界点。最后，我们报告了一些数值结果，以显示所提算法的有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.