The complexity of high-order predictor-corrector methods for solving sufficient linear complementarity problems

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 1998-01-01 DOI:10.1080/10556789808805721

J. Stoer, Martin Wechs

引用次数: 11

Abstract

Recently the authors of this paper and S. Mizuno described a class of infeasible-interiorpoint methods for solving linear complementarity problems that are sufficient in the sense of R.W. Cottle, J.-S. Pang and V. Venkateswaran (1989) Sufficient matrices and the linear complementarity problemLinear Algebra AppL 114/115,231-249. It was shown that these methods converge superlinearly with an arbitrarily high order even for degenerate problems or problems without strictly complementary solution. In this paper the complexity of these methods is investigated. It is shown that all these methods, if started appropriately, need predictor-corrector steps to find an e-solution, and only steps, if the problem has strictly interior points. HereK is the sufficiency parameter of the complementarity problem.

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求解充分线性互补问题的高阶预测校正方法的复杂性

最近，本文的作者和S. Mizuno描述了一类求解线性互补问题的不可行内点方法，这些方法在R.W. Cottle, J.-S.意义上是充分的。彭文华(1989)充分矩阵与线性互补问题。线性代数，vol . 14(1): 1- 3。证明了这些方法即使对于退化问题或无严格互补解的问题也具有任意高阶的超线性收敛性。本文研究了这些方法的复杂性。结果表明，所有这些方法，如果适当地开始，都需要预测校正步骤来找到e解，如果问题有严格的内点，则只需步骤。这里，ek是互补问题的充分性参数。

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.