On Proximal Algorithms with Inertial Effects Beyond Monotonicity

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-10-13 DOI:10.1080/01630563.2023.2266762

Alfredo N. Iusem, R. T. Marcavillaca

引用次数: 0

Abstract

AbstractInertial procedures attached to classical methods for solving monotone inclusion and optimization problems, which arise from an implicit discretization of second-order differential equations, have shown a remarkable acceleration effect with respect to these classical algorithms. Among these classical methods, one can mention steepest descent, alternate directions, and the proximal point methods. For the problem of finding zeroes of set-valued operators, the convergence analysis of all existing inertial-proximal methods requires the monotonicity of the operator. We present here a new inertial-proximal point algorithm for finding zeroes of set-valued operators, whose convergence is established for a relevant class of nonmonotone operators, namely the hypomonotone ones.KEYWORDS: Generalized monotone operatorshypomonotone operatorsinertial methodsproximal point methodMATHEMATICS SUBJECT CLASSIFICATION: 90C2590C3047H05

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超越单调性的惯性效应的近端算法

求解二阶微分方程隐式离散化引起的单调包含和优化问题的经典方法所附的积分过程，相对于这些经典算法显示出显著的加速效应。在这些经典方法中，可以提到最陡下降法、交替方向法和近点法。对于集值算子的寻零问题，现有的所有积分逼近方法的收敛性分析都要求算子的单调性。本文提出了一种求集值算子零点的新算法，该算法对一类相关的非单调算子即次单调算子证明了收敛性。关键词:广义单调算子;拟单调算子;正弦方法;近似点法

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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.