RAIRO-Oper. Res. 42 (2008) 157-198
DOI: 10.1051/ro:2008008

Asymptotic analysis of the trajectories of the logarithmic barrier algorithm without constraint qualifications

A. El Afia¹, A. Benchakroun², J.-P. Dussault³ and K. El Yassini<sup>4

1</sup>  Université Mohammed V, Souisi, ENSIAS, Rabat, Maroc; elafia@ensias.ma
²  Université de Sherbrooke, Dép. d'informatique, Canada; Abdelhamid.Benchakroun@usherbrooke.ca
³  Université de Sherbrooke, Dép. d'informatique, Canada; Jean-Pierre.Dussault@usherbrooke.ca
⁴  Université Moulay Ismail, Faculté des Sciences à Meknès, Maroc; Khalid.ElYassini@usherbrooke.ca

(Received October 16, 2006 Published online 17 May 2008.)

Abstract
In this paper, we study the differentiability of the trajectories of the logarithmic barrier algorithm for a nonlinear program when the set of the Karush-Kuhn-Tucker multiplier vectors is empty owing to the fact that the constraint qualifications are not satisfied.

Mathematics Subject Classification. 90C30.

Key words: Logarithmic barrier, Penalty algorithms.


© EDP Sciences, ROADEF, SMAI 2008