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A logarithm barrier methodfor semi-definite programming

Published online by Cambridge University Press:  17 May 2008

Jean-Pierre Crouzeix  and
Bachir Merikhi
Jean-Pierre Crouzeix
Affiliation:
LIMOS, Université Blaise Pascal, Campus des Cézaux, 63174 Aubière, France; jp.crouzeix@isima.fr
Bachir Merikhi
Affiliation:
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
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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.

Keywords

Linear semi-definite programmingbarrier methodsline-search.

Information

Type
Research Article
Information
RAIRO - Operations Research , Volume 42 , Issue 2: CIRO 05 , April 2008 , pp. 123 - 139
Copyright
© EDP Sciences, ROADEF, SMAI, 2008

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References

Alizadeh, F., Interior point methods in semi-definite programming with application to combinatorial optimization. SIAM J. Optim. 5 (1995) 13–55. CrossRef
Alizadeh, F., Haberly, J.-P., and Overton, M.-L., Primal-dual interior-point methods for semi-definite programming, convergence rates, stability and numerical results. SIAM J. Optim. 8 (1998) 746–768. CrossRef
Benterki, D., Crouzeix, J.-P., and Merikhi, B., A numerical implementation of an interior point method for semi-definite programming. Pesquisa Operacional 23–1 (2003) 49–59. CrossRef
J.-F. Bonnans, J.-C. Gilbert, C. Lemaréchal, and C. Sagastizàbal, Numerical optimization, theoretical and practical aspects. Mathematics and Applications 27, Springer-Verlag, Berlin (2003).
Crouzeix, J.-P. and Seeger, A., New bounds for the extreme values of a finite sample of real numbers. J. Math. Anal. Appl. 197 (1996) 411–426. CrossRef
Kojima, M., Shindoh, S., and Hara, S., Interior point methods for the monotone semi-definite linear complementarity problem in symmetric matrices. SIAM J. Optim. 7 (1997) 86–125. CrossRef
Overton, M. and Wolkowicz, H., Semi-definite programming. Math. program. Serie B 77 (1997) 105–109.
R.T. Rockafellar, Convex analysis. Princeton University Press, New Jerzey (1970).
Vanderberghe, L. and Boyd, S., Positive definite programming. SIAM Review 38 (1996) 49–95. CrossRef
Wolkowicz, H. and Styan, G.-P.-H., Bounds for eigenvalues using traces. Linear Algebra Appl. 29 (1980) 471–506. CrossRef