Issue RAIRO-Oper. Res. Volume 43, Number 2, April-June 2009 Page(s) 189 - 199 DOI 10.1051/ro/2009011 Published online 28 April 2009

RAIRO-Oper. Res. 43 (2009) 189-199
DOI: 10.1051/ro/2009011

Kernel-function Based Algorithms for Semidefinite Optimization

M. EL Ghami¹, Y.Q. Bai² and C. roos<sup>3

1</sup>  Department of Informatics, University of Bergen,Post Box 7803 5020 Bergen, Norway; melghami@ii.uib.no
²  Department of Mathematics, Shanghai University, Shanghai, 200444, P.R. China; yqbai@shu.edu.cn
³  Faculty of Electrical Engineering, Mathematics, and Computer Science, Delft University of Technology, P.O. Box 5031, 2600 GA Delft, The Netherlands; C.Roos@ewi.tudelft.nl

Received October 10, 2007. Accepted January 27, 2009. Published online 28 April 2009

Abstract
Recently, Y.Q. Bai, M. El Ghami and C. Roos [3] introduced a new class of so-called eligible kernel functions which are defined by some simple conditions. The authors designed primal-dual interior-point methods for linear optimization (LO) based on eligible kernel functions and simplified the analysis of these methods considerably. In this paper we consider the semidefinite optimization (SDO) problem and we generalize the aforementioned results for LO to SDO. The iteration bounds obtained are analogous to the results in [3] for LO.

Mathematics Subject Classification. 90C22, 90C31.

Key words: Semidefinite optimization, interior-point methods, primal-dual method, complexity.


© EDP Sciences, ROADEF, SMAI 2009

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