A Unified Approach to Infeasible-Interior-Point Algorithms via Geometrical Linear Complementarity Problems.
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| Title: | A Unified Approach to Infeasible-Interior-Point Algorithms via Geometrical Linear Complementarity Problems. |
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| Authors: | Mizuno, Shinji, Jarre, F., Stoer, J. |
| Source: | Applied Mathematics & Optimization. 1996, Vol. 33 Issue 3, p315. 27p. |
| Subjects: | Interior-point methods, Linear programming, Linear complementarity problem |
| Abstract: | There are many interior-point algorithms for LP (linear programming), QP (quadratic programming), and LCPs (linear complementarity problems). While the algebraic definitions of these problems are different from each other, we show that they are all of the same general form when we define the problems geometrically. We derive some basic properties related to such geometrical (monotone) LCPs and based on these properties, we propose and analyze a simple infeasible-interior-point algorithm for solving geometrical LCPs. The algorithm can solve any instance of the above classes without making any assumptions on the problem. It features global convergence, polynomial-time convergence if there is a solution that is "smaller" than the initial point, and quadratic convergence if there is a strictly complementary solution. [ABSTRACT FROM AUTHOR] |
| Copyright of Applied Mathematics & Optimization is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Items | – Name: Title Label: Title Group: Ti Data: A Unified Approach to Infeasible-Interior-Point Algorithms via Geometrical Linear Complementarity Problems. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Mizuno%2C+Shinji%22">Mizuno, Shinji</searchLink><br /><searchLink fieldCode="AR" term="%22Jarre%2C+F%2E%22">Jarre, F.</searchLink><br /><searchLink fieldCode="AR" term="%22Stoer%2C+J%2E%22">Stoer, J.</searchLink> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Applied+Mathematics+%26+Optimization%22">Applied Mathematics & Optimization</searchLink>. 1996, Vol. 33 Issue 3, p315. 27p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Interior-point+methods%22">Interior-point methods</searchLink><br /><searchLink fieldCode="DE" term="%22Linear+programming%22">Linear programming</searchLink><br /><searchLink fieldCode="DE" term="%22Linear+complementarity+problem%22">Linear complementarity problem</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: There are many interior-point algorithms for LP (linear programming), QP (quadratic programming), and LCPs (linear complementarity problems). While the algebraic definitions of these problems are different from each other, we show that they are all of the same general form when we define the problems geometrically. We derive some basic properties related to such geometrical (monotone) LCPs and based on these properties, we propose and analyze a simple infeasible-interior-point algorithm for solving geometrical LCPs. The algorithm can solve any instance of the above classes without making any assumptions on the problem. It features global convergence, polynomial-time convergence if there is a solution that is "smaller" than the initial point, and quadratic convergence if there is a strictly complementary solution. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Applied Mathematics & Optimization is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1007/BF01204707 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 27 StartPage: 315 Subjects: – SubjectFull: Interior-point methods Type: general – SubjectFull: Linear programming Type: general – SubjectFull: Linear complementarity problem Type: general Titles: – TitleFull: A Unified Approach to Infeasible-Interior-Point Algorithms via Geometrical Linear Complementarity Problems. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Mizuno, Shinji – PersonEntity: Name: NameFull: Jarre, F. – PersonEntity: Name: NameFull: Stoer, J. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 05 Text: 1996 Type: published Y: 1996 Identifiers: – Type: issn-print Value: 00954616 Numbering: – Type: volume Value: 33 – Type: issue Value: 3 Titles: – TitleFull: Applied Mathematics & Optimization Type: main |
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