The effect of the parameter of the potential function on the conditioning of interior point methods

Adama Coulibaly; Jean-Pierre Crouzeix

RAIRO - Operations Research (2010)

  • Volume: 37, Issue: 2, page 99-117
  • ISSN: 0399-0559

Abstract

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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.

How to cite

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Coulibaly, Adama, and Crouzeix, Jean-Pierre. "Les effets de l'exposant de la fonction barrière multiplicative dans les méthodes de points intérieurs." RAIRO - Operations Research 37.2 (2010): 99-117. <http://eudml.org/doc/105285>.

@article{Coulibaly2010,
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. },
author = {Coulibaly, Adama, Crouzeix, Jean-Pierre},
journal = {RAIRO - Operations Research},
keywords = {Interior point methods; Karmarkar algorithm; multiplicative and additive potential functions; barrier function.; interior point methods; barrier function; convexity},
language = {fre},
month = {3},
number = {2},
pages = {99-117},
publisher = {EDP Sciences},
title = {Les effets de l'exposant de la fonction barrière multiplicative dans les méthodes de points intérieurs},
url = {http://eudml.org/doc/105285},
volume = {37},
year = {2010},
}

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
DA - 2010/3//
PB - EDP Sciences
VL - 37
IS - 2
SP - 99
EP - 117
AB - 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.
LA - fre
KW - Interior point methods; Karmarkar algorithm; multiplicative and additive potential functions; barrier function.; interior point methods; barrier function; convexity
UR - http://eudml.org/doc/105285
ER -

References

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