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Une procédure de purificationpour les problèmes de complémentarité linéaire, monotones

Published online by Cambridge University Press:  15 April 2004

Abderrahim Kadiri  and
Adnan Yassine
Abderrahim Kadiri
Affiliation:
LMAH, Université du Havre, BP 540, 76058 Le Havre, France ; [email protected].
Adnan Yassine
Affiliation:
LMAH, Université du Havre, BP 540, 76058 Le Havre, France ; [email protected].
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Abstract

Dans cet article, nous proposons une nouvelle méthode de purification pour les problèmes de complémentarité linéaire, monotones. Cette méthode associe à chaque itéré de la suite, générée par une méthode de points intérieurs, une base non nécessairement réalisable. Nous montrons que, sous les hypothèses de complémentarité stricte et de non dégénérescence, la suite des bases converge en un nombre fini d'itérations vers une base optimale qui donne une solution exacte du problème. Le procédé adopté sert également à préconditionner l'algorithme de gradient conjugué lors du calcul de la direction de Newton.

Keywords

Problèmes de complémentarité linéaireméthodes de points intérieurspurificationsolution exacteconvergence finiegradient conjuguépréconditionnementprogrammation quadratique convexe.
Type
Research Article
Information
RAIRO - Operations Research , Volume 38 , Issue 1 , January 2004 , pp. 63 - 83
Copyright
© EDP Sciences, 2004

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