Warm Start and ε-Subgradients in a Cutting Plane Scheme for Block-Angular Linear Programs
This paper addresses the issues involved with an interior point-based decomposition applied to the solution of linear programs with a block-angular structure. Unlike classical decomposition schemes that use the simplex method to solve subproblems, the approach presented in this paper employs a prima...
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| Veröffentlicht in: | Computational optimization and applications Jg. 14; H. 1; S. 17 - 36 |
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| Hauptverfasser: | , |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
01.07.1999
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| ISSN: | 0926-6003, 1573-2894 |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | This paper addresses the issues involved with an interior point-based decomposition applied to the solution of linear programs with a block-angular structure. Unlike classical decomposition schemes that use the simplex method to solve subproblems, the approach presented in this paper employs a primal-dual infeasible interior point method. The above-mentioned algorithm offers a perfect measure of the distance to optimality, which is exploited to terminate the algorithm earlier (with a rather loose optimality tolerance) and to generate epsilon -subgradients. In the decomposition scheme, subproblems are sequentially solved for varying objective functions. It is essential to be able to exploit the optimal solution of the previous problem when solving a subsequent one (with a modified objective). A warm start routine is described that deals with this problem. The proposed approach has been implemented within the context of two optimization codes freely available for research use: the Analytic Center Cutting Plane Method (ACCPM)-interior point based decomposition algorithm and the Higher Order Primal-Dual Method (HOPDM) - general purpose interior point LP solver. Computational results are given to illustrate the potential advantages of the approach applied to the solution of very large structured linear programs. |
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| Bibliographie: | ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23 |
| ISSN: | 0926-6003 1573-2894 |
| DOI: | 10.1023/A:1008748810765 |