RAIRO-Oper. Res. 42 (2008) 123-139
DOI: 10.1051/ro:2008005

A logarithm barrier method for semi-definite programming

Jean-Pierre Crouzeix¹ and Bachir Merikhi<sup>2

1</sup>  LIMOS, Université Blaise Pascal, Campus des Cézaux, 63174 Aubière, France; jp.crouzeix@isima.fr
²  Laboratoire d'optimisation, Université Ferhat Abbas, Algérie; the research of this author has been made possible thanks to a PROFAS grant and the hospitality of Université Blaise Pascal. b_merikhi@yahoo.fr

(Received September 01, 2006. Accepted September 01, 2006 Published online 17 May 2008.)

Abstract
This paper presents a logarithmic barrier method for solving a semi-definite linear program. The descent direction is the classical Newton direction. We propose alternative ways to determine the step-size along the direction which are more efficient than classical line-searches.

Mathematics Subject Classification. 90C22, 90C05, 90C51.

Key words: Linear semi-definite programming, barrier methods, line-search.


© EDP Sciences, ROADEF, SMAI 2008