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| HAL : inria-00442293, version 4 |
| Voir la fiche détaillée |  BibTeX,EndNote,... |
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| Versions disponibles | v1 (19-12-2009) | v2 (11-04-2010) | v3 (27-09-2010) | v4 (28-12-2010) |
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| Nonconvergence of the plain Newton-min algorithm for linear complementarity problems with a P-matrix --- The full report. |
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Ibtihel Ben Gharbia 1Jean Charles Gilbert 1 |
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| (2010) |
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| The plain Newton-min algorithm to solve the linear complementarity problem (LCP for short) $0\leq x\perp(Mx+q)\geq0$ can be viewed as a nonsmooth Newton algorithm without globalization technique to solve the system of piecewise linear equations $\min(x,Mx+q)=0$, which is equivalent to the LCP. When $M$ is an $\Mmat$-matrix of order~$n$, the algorithm is known to converge in at most $n$ iterations. We show in this paper that this result no longer holds when $M$ is a $\Pmat$-matrix of order~$\geq\nobreak3$, since then the algorithm may cycle. $\Pmat$-matrices are interesting since they are those ensuring the existence and uniqueness of the solution to the LCP for an arbitrary~$q$. Incidentally, convergence occurs for a $\Pmat$-matrix of order~$1$ or~$2$. |
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| 1 : | ESTIME (INRIA Rocquencourt) |
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INRIA |
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| Domaine | : | Mathématiques/Optimisation et contrôle |
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| Linear complementarity problem – Newton's method – Nonconvergence – Nonsmooth function – M-matrix – P-matrix |
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| Liste des fichiers attachés à ce document : | |||||
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| inria-00442293, version 4 | |
| http://hal.inria.fr/inria-00442293 | |
| oai:hal.inria.fr:inria-00442293 | |
| Contributeur : Jean Charles Gilbert | |
| Soumis le : Mardi 28 Décembre 2010, 17:39:35 | |
| Dernière modification le : Mardi 8 Mars 2011, 11:11:55 | |
