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.
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 . Cet exposant est, de façon générale, choisi supérieur au nombre de variables du problème. Nous montrons dans cet article que l’on peut utiliser des valeurs de plus petites que . Ceci permet d’améliorer le conditionnement de la méthode au voisinage de la solution optimale.
Mots-clés : interior point methods, karmarkar algorithm, multiplicative and additive potential functions, barrier function
@article{RO_2003__37_2_99_0, 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://archive.numdam.org/articles/10.1051/ro:2003016/} }
TY - JOUR AU - Coulibaly, Adama AU - Crouzeix, Jean-Pierre TI - Les effets de l'exposant de la fonction barrière multiplicative dans les méthodes de points intérieurs JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2003 SP - 99 EP - 117 VL - 37 IS - 2 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ro:2003016/ DO - 10.1051/ro:2003016 LA - fr ID - RO_2003__37_2_99_0 ER -
%0 Journal Article %A Coulibaly, Adama %A Crouzeix, Jean-Pierre %T Les effets de l'exposant de la fonction barrière multiplicative dans les méthodes de points intérieurs %J RAIRO - Operations Research - Recherche Opérationnelle %D 2003 %P 99-117 %V 37 %N 2 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ro:2003016/ %R 10.1051/ro:2003016 %G fr %F RO_2003__37_2_99_0
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, Volume 37 (2003) no. 2, pp. 99-117. doi : 10.1051/ro:2003016. http://archive.numdam.org/articles/10.1051/ro:2003016/
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