{"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}
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.
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.
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