求解充分线性互补问题的高阶预测校正方法的复杂性

IF 1.4 3区数学 Q3 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Optimization Methods & Software Pub Date : 1998-01-01 DOI:10.1080/10556789808805721

J. Stoer, Martin Wechs

{"title":"求解充分线性互补问题的高阶预测校正方法的复杂性","authors":"J. Stoer, Martin Wechs","doi":"10.1080/10556789808805721","DOIUrl":null,"url":null,"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.","PeriodicalId":54673,"journal":{"name":"Optimization Methods & Software","volume":"59 1","pages":"393-417"},"PeriodicalIF":1.4000,"publicationDate":"1998-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"11","resultStr":"{\"title\":\"The complexity of high-order predictor-corrector methods for solving sufficient linear complementarity problems\",\"authors\":\"J. Stoer, Martin Wechs\",\"doi\":\"10.1080/10556789808805721\",\"DOIUrl\":null,\"url\":null,\"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.\",\"PeriodicalId\":54673,\"journal\":{\"name\":\"Optimization Methods & Software\",\"volume\":\"59 1\",\"pages\":\"393-417\"},\"PeriodicalIF\":1.4000,\"publicationDate\":\"1998-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"11\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Optimization Methods & Software\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://doi.org/10.1080/10556789808805721\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"COMPUTER SCIENCE, SOFTWARE ENGINEERING\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Optimization Methods & Software","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1080/10556789808805721","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, SOFTWARE ENGINEERING","Score":null,"Total":0}

引用次数: 11

摘要

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。

查看原文本刊更多论文

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

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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Optimization Methods & Software 工程技术-计算机：软件工程

CiteScore

4.50

自引率

0.00%

发文量

审稿时长

7 months

期刊介绍： Optimization Methods and Software publishes refereed papers on the latest developments in the theory and realization of optimization methods, with particular emphasis on the interface between software development and algorithm design. Topics include: Theory, implementation and performance evaluation of algorithms and computer codes for linear, nonlinear, discrete, stochastic optimization and optimal control. This includes in particular conic, semi-definite, mixed integer, network, non-smooth, multi-objective and global optimization by deterministic or nondeterministic algorithms. Algorithms and software for complementarity, variational inequalities and equilibrium problems, and also for solving inverse problems, systems of nonlinear equations and the numerical study of parameter dependent operators. Various aspects of efficient and user-friendly implementations: e.g. automatic differentiation, massively parallel optimization, distributed computing, on-line algorithms, error sensitivity and validity analysis, problem scaling, stopping criteria and symbolic numeric interfaces. Theoretical studies with clear potential for applications and successful applications of specially adapted optimization methods and software to fields like engineering, machine learning, data mining, economics, finance, biology, or medicine. These submissions should not consist solely of the straightforward use of standard optimization techniques.