A study of search directions in primal-dual interior-point methods for semidefinite programming

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 1999-01-01 DOI:10.1080/10556789908805745

M. Todd

引用次数: 122

Abstract

We discuss several different search directions which can be used in primal-dual interior-point methods for semidefinite programming problems and investigate their theoretical properties, including scale invariance, primal-dual symmetry, and whether they always generate well-defined directions. Among the directions satisfying all but at most two of these desirable properties are the Alizadeh-Haeberly-Overton, Helmberg-Rendl-Vanderbei-Wolkowicz/Kojima-Shindoh-HaralMonteiro, Nesterov-Todd, Gu, and Toh directions, as well as directions we will call the MTW and Half directions. The first five of these appear to be the best in our limited computational testing also.

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半定规划中原始-对偶内点法搜索方向的研究

讨论了用于半确定规划问题的原始-对偶内点方法的几种不同的搜索方向，并研究了它们的理论性质，包括尺度不变性、原始-对偶对称性以及它们是否总是生成良好定义的方向。在满足所有这些理想性质的方向中，除了最多两个之外，还有alizadeh - haebery - overton, Helmberg-Rendl-Vanderbei-Wolkowicz/Kojima-Shindoh-HaralMonteiro, Nesterov-Todd, Gu和Toh方向，以及我们称之为MTW和Half方向。在我们有限的计算测试中，前五个似乎也是最好的。

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.