An alternate gradient method for optimization problems with orthogonality constraints

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-01-01 DOI:10.3934/NACO.2021003

Yanmei Sun, Yakui Huang

引用次数: 1

Abstract

In this paper, we propose a new alternate gradient (AG) method to solve a class of optimization problems with orthogonal constraints. In particular, our AG method alternately takes several gradient reflection steps followed by one gradient projection step. It is proved that any accumulation point of the iterations generated by the AG method satisfies the first-order optimal condition. Numerical experiments show that our method is efficient.

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正交约束优化问题的交替梯度法

本文提出了一种新的交替梯度(AG)方法来解决一类具有正交约束的优化问题。特别是，我们的AG方法交替地采用几个梯度反射步骤，然后是一个梯度投影步骤。证明了AG方法生成的迭代的任何累加点都满足一阶最优条件。数值实验表明，该方法是有效的。

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

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.