{"title":"与P - o矩阵相关的垂直线性互补问题","authors":"Aniekan Ebiefung","doi":"10.1080/10556789908805739","DOIUrl":null,"url":null,"abstract":"We show that the vertical linear complementarity problem can be solved, under certain conditions, by solving a perturbed problem when the associated matrix is a vertical block P o-matrix. The main conditions do not depend on nondegeneracy of the problem or on the matrix class to which the P o matrix may also belong. In the special case of the K o-matrices, the least element solution of the perturbed problem converges to the least element solution of the original problem.","PeriodicalId":54673,"journal":{"name":"Optimization Methods & Software","volume":null,"pages":null},"PeriodicalIF":1.4000,"publicationDate":"1999-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"The vertical linear complementarity problem associated with P o-matrices\",\"authors\":\"Aniekan Ebiefung\",\"doi\":\"10.1080/10556789908805739\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We show that the vertical linear complementarity problem can be solved, under certain conditions, by solving a perturbed problem when the associated matrix is a vertical block P o-matrix. The main conditions do not depend on nondegeneracy of the problem or on the matrix class to which the P o matrix may also belong. In the special case of the K o-matrices, the least element solution of the perturbed problem converges to the least element solution of the original problem.\",\"PeriodicalId\":54673,\"journal\":{\"name\":\"Optimization Methods & Software\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.4000,\"publicationDate\":\"1999-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Optimization Methods & Software\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://doi.org/10.1080/10556789908805739\",\"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/10.1080/10556789908805739","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 vertical linear complementarity problem associated with P o-matrices
We show that the vertical linear complementarity problem can be solved, under certain conditions, by solving a perturbed problem when the associated matrix is a vertical block P o-matrix. The main conditions do not depend on nondegeneracy of the problem or on the matrix class to which the P o matrix may also belong. In the special case of the K o-matrices, the least element solution of the perturbed problem converges to the least element solution of the original 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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