Interior-Point Solver for Large-Scale Quadratic Programming Problems with Bound Constraints.
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| Title: | Interior-Point Solver for Large-Scale Quadratic Programming Problems with Bound Constraints. |
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| Authors: | CAFIERI, S.1, D'APUZZO, M.2, MARINO, M.3, MUCHERINO, A.1, TORALDO, G.3 |
| Source: | Journal of Optimization Theory & Applications. Apr2006, Vol. 129 Issue 1, p55-75. 21p. |
| Subjects: | Quadratic programming, Nonlinear programming, Iterative methods (Mathematics), Linear systems, Algorithms, Factorization, Factors (Algebra), Linear differential equations, Mathematics |
| Abstract: | In this paper, we present an interior-point algorithm for large and sparse convex quadratic programming problems with bound constraints. The algorithm is based on the potential reduction method and the use of iterative techniques to solve the linear system arising at each iteration. The global convergence properties of the potential reduction method are reassessed in order to take into account the inexact solution of the inner system. We describe the iterative solver, based on the conjugate gradient method with a limited-memory incomplete Cholesky factorization as preconditioner. Furthermore, we discuss some adaptive strategies for the fill-in and accuracy requirements that we use in solving the linear systems in order to avoid unnecessary inner iterations when the iterates are far from the solution. Finally, we present the results of numerical experiments carried out to verify the effectiveness of the proposed strategies. We consider randomly generated sparse problems without a special structure. Also, we compare the proposed algorithm with the MOSEK solver. [ABSTRACT FROM AUTHOR] |
| Copyright of Journal of Optimization Theory & Applications 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 |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 23965065 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Interior-Point Solver for Large-Scale Quadratic Programming Problems with Bound Constraints. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22CAFIERI%2C+S%2E%22">CAFIERI, S.</searchLink><relatesTo>1</relatesTo><br /><searchLink fieldCode="AR" term="%22D'APUZZO%2C+M%2E%22">D'APUZZO, M.</searchLink><relatesTo>2</relatesTo><br /><searchLink fieldCode="AR" term="%22MARINO%2C+M%2E%22">MARINO, M.</searchLink><relatesTo>3</relatesTo><br /><searchLink fieldCode="AR" term="%22MUCHERINO%2C+A%2E%22">MUCHERINO, A.</searchLink><relatesTo>1</relatesTo><br /><searchLink fieldCode="AR" term="%22TORALDO%2C+G%2E%22">TORALDO, G.</searchLink><relatesTo>3</relatesTo> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Optimization+Theory+%26+Applications%22">Journal of Optimization Theory & Applications</searchLink>. Apr2006, Vol. 129 Issue 1, p55-75. 21p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Quadratic+programming%22">Quadratic programming</searchLink><br /><searchLink fieldCode="DE" term="%22Nonlinear+programming%22">Nonlinear programming</searchLink><br /><searchLink fieldCode="DE" term="%22Iterative+methods+%28Mathematics%29%22">Iterative methods (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Linear+systems%22">Linear systems</searchLink><br /><searchLink fieldCode="DE" term="%22Algorithms%22">Algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Factorization%22">Factorization</searchLink><br /><searchLink fieldCode="DE" term="%22Factors+%28Algebra%29%22">Factors (Algebra)</searchLink><br /><searchLink fieldCode="DE" term="%22Linear+differential+equations%22">Linear differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics%22">Mathematics</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: In this paper, we present an interior-point algorithm for large and sparse convex quadratic programming problems with bound constraints. The algorithm is based on the potential reduction method and the use of iterative techniques to solve the linear system arising at each iteration. The global convergence properties of the potential reduction method are reassessed in order to take into account the inexact solution of the inner system. We describe the iterative solver, based on the conjugate gradient method with a limited-memory incomplete Cholesky factorization as preconditioner. Furthermore, we discuss some adaptive strategies for the fill-in and accuracy requirements that we use in solving the linear systems in order to avoid unnecessary inner iterations when the iterates are far from the solution. Finally, we present the results of numerical experiments carried out to verify the effectiveness of the proposed strategies. We consider randomly generated sparse problems without a special structure. Also, we compare the proposed algorithm with the MOSEK solver. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Journal of Optimization Theory & Applications 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/s10957-006-9043-6 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 21 StartPage: 55 Subjects: – SubjectFull: Quadratic programming Type: general – SubjectFull: Nonlinear programming Type: general – SubjectFull: Iterative methods (Mathematics) Type: general – SubjectFull: Linear systems Type: general – SubjectFull: Algorithms Type: general – SubjectFull: Factorization Type: general – SubjectFull: Factors (Algebra) Type: general – SubjectFull: Linear differential equations Type: general – SubjectFull: Mathematics Type: general Titles: – TitleFull: Interior-Point Solver for Large-Scale Quadratic Programming Problems with Bound Constraints. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: CAFIERI, S. – PersonEntity: Name: NameFull: D'APUZZO, M. – PersonEntity: Name: NameFull: MARINO, M. – PersonEntity: Name: NameFull: MUCHERINO, A. – PersonEntity: Name: NameFull: TORALDO, G. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 04 Text: Apr2006 Type: published Y: 2006 Identifiers: – Type: issn-print Value: 00223239 Numbering: – Type: volume Value: 129 – Type: issue Value: 1 Titles: – TitleFull: Journal of Optimization Theory & Applications Type: main |
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