用于非凸最小化的布雷格曼惯性前向-反射-后向方法

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-12-16 DOI:10.1007/s10898-023-01348-y

Xianfu Wang, Ziyuan Wang

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引用次数: 0

摘要

我们提出了一种针对非凸复合问题的 Bregman 惯性前向反射后向方法（BiFRB）。假设广义凹 Kurdyka-Łojasiewicz 属性，我们得到了 BiFRB 的顺序收敛性，以及函数值和实际序列的收敛率。我们的分析有一个显著特点，那就是我们仔细处理了优点函数参数，规避了惯性参数的通常限制性假设。我们还提出了布雷格曼子问题的公式，这不仅是对 BiFRB 的补充，也是对 Boţ-Csetnek-László 和 Boţ-Csetnek 工作的补充。我们进行了数字模拟，以评估我们提出的算法的性能。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

A Bregman inertial forward-reflected-backward method for nonconvex minimization

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A Bregman inertial forward-reflected-backward method for nonconvex minimization

We propose a Bregman inertial forward-reflected-backward (BiFRB) method for nonconvex composite problems. Assuming the generalized concave Kurdyka-Łojasiewicz property, we obtain sequential convergence of BiFRB, as well as convergence rates on both the function value and actual sequence. One distinguishing feature in our analysis is that we utilize a careful treatment of merit function parameters, circumventing the usual restrictive assumption on the inertial parameters. We also present formulae for the Bregman subproblem, supplementing not only BiFRB but also the work of Boţ-Csetnek-László and Boţ-Csetnek. Numerical simulations are conducted to evaluate the performance of our proposed algorithm.

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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.