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gradient conjugué

RAIRO - Operations Research (1)

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Une procédure de purificationpour les problèmes de complémentarité linéaire, monotones
Abderrahim Kadiri, Adnan Yassine
Journal:

RAIRO - Operations Research / Volume 38 / Issue 1 / January 2004

Published online by Cambridge University Press:

15 April 2004, pp. 63-83

Print publication:

January 2004
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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.