Improving an interior-point algorithm for multicommodity flows by quadratic regularizations
One of the best approaches for some classes of multicommodity flow problems is a specialized interior‐point method that solves the normal equations by a combination of Cholesky factorizations and preconditioned conjugate gradient. Its efficiency depends on the spectral radius—in [0,1)—of a certain m...
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| Vydáno v: | Networks Ročník 59; číslo 1; s. 117 - 131 |
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| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Hoboken
Wiley Subscription Services, Inc., A Wiley Company
01.01.2012
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| Témata: | |
| ISSN: | 0028-3045, 1097-0037 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | One of the best approaches for some classes of multicommodity flow problems is a specialized interior‐point method that solves the normal equations by a combination of Cholesky factorizations and preconditioned conjugate gradient. Its efficiency depends on the spectral radius—in [0,1)—of a certain matrix in the definition of the preconditioner. In a recent work, the authors improved this algorithm (i.e., reduced the spectral radius) for general block‐angular problems by adding a quadratic regularization to the logarithmic barrier. This barrier was shown to be self‐concordant, which guarantees the convergence and polynomial complexity of the algorithm. In this work, we focus on linear multicommodity problems, a particular case of primal block‐angular ones. General results are tailored for multicommodity flows, allowing a local sensitivity analysis on the effect of the regularization. Extensive computational results on some standard and some difficult instances, testing several regularization strategies, are also provided. These results show that the regularized interior‐point algorithm is more efficient than the nonregularized one. From this work it can be concluded that, if interior‐point methods based on conjugate gradients are used, linear multicommodity flow problems are most efficiently solved as a sequence of quadratic ones. © 2011 Wiley Periodicals, Inc. NETWORKS, 2012 |
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| Bibliografie: | Government of Catalonia - No. SGR-2009-1122 ark:/67375/WNG-4P473TKB-S MICINN - No. MTM2009-08747 istex:BD7A9CCB525452931F8DD4EF877978795F08E2ED MEC - No. MTM2006-05550 ArticleID:NET20483 |
| ISSN: | 0028-3045 1097-0037 |
| DOI: | 10.1002/net.20483 |