A Graph-based Decentralization Proposal for Convex Non Linear Separable Problems with Linear Constraints.
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| Title: | A Graph-based Decentralization Proposal for Convex Non Linear Separable Problems with Linear Constraints. |
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| Authors: | Cerda, Jaime1 jcerda@umich.mx, Graff, Mario1 mgraffg@dep.fie.umich.mx |
| Source: | Proceedings of the World Congress on Engineering & Computer Science 2013 Volume I. 2013, p1-5. 5p. |
| Subjects: | Nonlinear theories, Nonlinear programming, Constraints (Physics), Sparse matrices, Graph theory |
| Abstract: | This document proposes several decentralization approaches for the Newton step graph-based model for convex non linear separable problems with linear constraints. The Newton step is well suited for this kind of problems, but when the problem size grows the NLP model will grow in a non linear manner. When this happens, the sparse matrix representation is the path to follow. Furthermore, decentralization schemes are suitable to keep the problem from growing exponentially. In this work a graph based method to achieve this decentralization is proposed. To this end, we have chosen to weak the links, which are part of the graph, as an alternative. These links eventually will guide the solution process in this approach, which implies to weak the links which are coupling the problems in order to achieve such decentralization. A deeper analysis of these links is done which leads to its complete understanding. It will be seen that the main effect of the link weakening operation is to allow the computation of the exact gradient. However, the solution will be reinforced by taking into account the second order information provided by the linking structure. Finally, different decentralisation schemes are presented based on the previous analysis. [ABSTRACT FROM AUTHOR] |
| Copyright of Proceedings of the World Congress on Engineering & Computer Science 2013 Volume I is the property of International Association of Engineers (IAENG) 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.) | |
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| Items | – Name: Title Label: Title Group: Ti Data: A Graph-based Decentralization Proposal for Convex Non Linear Separable Problems with Linear Constraints. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Cerda%2C+Jaime%22">Cerda, Jaime</searchLink><relatesTo>1</relatesTo><i> jcerda@umich.mx</i><br /><searchLink fieldCode="AR" term="%22Graff%2C+Mario%22">Graff, Mario</searchLink><relatesTo>1</relatesTo><i> mgraffg@dep.fie.umich.mx</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Proceedings+of+the+World+Congress+on+Engineering+%26+Computer+Science+2013+Volume+I%22">Proceedings of the World Congress on Engineering & Computer Science 2013 Volume I</searchLink>. 2013, p1-5. 5p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Nonlinear+theories%22">Nonlinear theories</searchLink><br /><searchLink fieldCode="DE" term="%22Nonlinear+programming%22">Nonlinear programming</searchLink><br /><searchLink fieldCode="DE" term="%22Constraints+%28Physics%29%22">Constraints (Physics)</searchLink><br /><searchLink fieldCode="DE" term="%22Sparse+matrices%22">Sparse matrices</searchLink><br /><searchLink fieldCode="DE" term="%22Graph+theory%22">Graph theory</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: This document proposes several decentralization approaches for the Newton step graph-based model for convex non linear separable problems with linear constraints. The Newton step is well suited for this kind of problems, but when the problem size grows the NLP model will grow in a non linear manner. When this happens, the sparse matrix representation is the path to follow. Furthermore, decentralization schemes are suitable to keep the problem from growing exponentially. In this work a graph based method to achieve this decentralization is proposed. To this end, we have chosen to weak the links, which are part of the graph, as an alternative. These links eventually will guide the solution process in this approach, which implies to weak the links which are coupling the problems in order to achieve such decentralization. A deeper analysis of these links is done which leads to its complete understanding. It will be seen that the main effect of the link weakening operation is to allow the computation of the exact gradient. However, the solution will be reinforced by taking into account the second order information provided by the linking structure. Finally, different decentralisation schemes are presented based on the previous analysis. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Proceedings of the World Congress on Engineering & Computer Science 2013 Volume I is the property of International Association of Engineers (IAENG) 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: Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 5 StartPage: 1 Subjects: – SubjectFull: Nonlinear theories Type: general – SubjectFull: Nonlinear programming Type: general – SubjectFull: Constraints (Physics) Type: general – SubjectFull: Sparse matrices Type: general – SubjectFull: Graph theory Type: general Titles: – TitleFull: A Graph-based Decentralization Proposal for Convex Non Linear Separable Problems with Linear Constraints. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Cerda, Jaime – PersonEntity: Name: NameFull: Graff, Mario IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 07 Text: 2013 Type: published Y: 2013 Identifiers: – Type: isbn-print Value: 9789881925237 Titles: – TitleFull: Proceedings of the World Congress on Engineering & Computer Science 2013 Volume I Type: main |
| ResultId | 1 |
