Les effets de l'exposant de la fonction barrière multiplicative dans les méthodes de points intérieurs

Coulibaly, Adama; Crouzeix, Jean-Pierre

doi:10.1051/ro:2003016

Coulibaly, Adama ; Crouzeix, Jean-Pierre

RAIRO - Operations Research - Recherche Opérationnelle, Tome 37 (2003) no. 2, pp. 99-117.

Résumé
Abstract

Les méthodes de points intérieurs en programmation linéaire connaissent un grand succès depuis l’introduction de l’algorithme de Karmarkar. La convergence de l’algorithme repose sur une fonction potentielle qui, sous sa forme multiplicative, fait apparaître un exposant $p$ . Cet exposant est, de façon générale, choisi supérieur au nombre de variables $n$ du problème. Nous montrons dans cet article que l’on peut utiliser des valeurs de $p$ plus petites que $n$ . Ceci permet d’améliorer le conditionnement de la méthode au voisinage de la solution optimale.

Potential functions in interior point methods are used to determine descent directions and to prove the convergence. They depend on a parameter which is usually taken equal to or greater than the size of the problem. Actually, smaller values give a better conditioning of the method near an optimal solution. This assertion is illustrated by a few numerical experiments.

Zbl

DOI : 10.1051/ro:2003016

Classification : 49M35, 90C05, 26B25
Mots clés : interior point methods, karmarkar algorithm, multiplicative and additive potential functions, barrier function

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     author = {Coulibaly, Adama and Crouzeix, Jean-Pierre},
     title = {Les effets de l'exposant de la fonction barri\`ere multiplicative dans les m\'ethodes de points int\'erieurs},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {99--117},
     publisher = {EDP-Sciences},
     volume = {37},
     number = {2},
     year = {2003},
     doi = {10.1051/ro:2003016},
     zbl = {1069.90108},
     language = {fr},
     url = {http://www.numdam.org/articles/10.1051/ro:2003016/}
}

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Coulibaly, Adama; Crouzeix, Jean-Pierre. Les effets de l'exposant de la fonction barrière multiplicative dans les méthodes de points intérieurs. RAIRO - Operations Research - Recherche Opérationnelle, Tome 37 (2003) no. 2, pp. 99-117. doi : 10.1051/ro:2003016. http://www.numdam.org/articles/10.1051/ro:2003016/

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