Interior point methods applied to optimization problems have known a remarkable evolution in the last decades. They are used with success in linear, quadratic and semidefinite programming. Among these methods, primal-dual central trajectory methods have a polynomial convergence and are credited of a good numerical behavior. In this paper, we propose a new central trajectory method where a relaxation parameter is introduced in order to give more flexibility to the theoretical and numerical aspects of the perturbed problems and accelerate the convergence of the algorithm. This claim is confirmed by numerical tests showing the good behavior of the algorithm which is proposed in this paper.
Accepté le :
DOI : 10.1051/ro/2014055
Mots clés : Linear programming, semidefinite programming, central trajectory Methods
@article{RO_2015__49_3_555_0,
author = {Samia, Kettab and Djamel, Benterki},
title = {A relaxed logarithmic barrier method for semidefinite programming},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {555--568},
publisher = {EDP-Sciences},
volume = {49},
number = {3},
year = {2015},
doi = {10.1051/ro/2014055},
mrnumber = {3349134},
zbl = {1327.90179},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/ro/2014055/}
}
TY - JOUR AU - Samia, Kettab AU - Djamel, Benterki TI - A relaxed logarithmic barrier method for semidefinite programming JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2015 SP - 555 EP - 568 VL - 49 IS - 3 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ro/2014055/ DO - 10.1051/ro/2014055 LA - en ID - RO_2015__49_3_555_0 ER -
%0 Journal Article %A Samia, Kettab %A Djamel, Benterki %T A relaxed logarithmic barrier method for semidefinite programming %J RAIRO - Operations Research - Recherche Opérationnelle %D 2015 %P 555-568 %V 49 %N 3 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ro/2014055/ %R 10.1051/ro/2014055 %G en %F RO_2015__49_3_555_0
Samia, Kettab; Djamel, Benterki. A relaxed logarithmic barrier method for semidefinite programming. RAIRO - Operations Research - Recherche Opérationnelle, Tome 49 (2015) no. 3, pp. 555-568. doi : 10.1051/ro/2014055. http://archive.numdam.org/articles/10.1051/ro/2014055/
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