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Kernel-function Based Algorithmsfor Semidefinite Optimization

Published online by Cambridge University Press:  28 April 2009

M. EL Ghami ,
Y. Q. Bai  and
C. Roos
M. EL Ghami
Affiliation:
Department of Informatics, University of Bergen,Post Box 7803 5020 Bergen, Norway; [email protected]
Y. Q. Bai
Affiliation:
Department of Mathematics, Shanghai University, Shanghai, 200444, P.R. China; [email protected]
C. Roos
Affiliation:
Faculty of Electrical Engineering, Mathematics, and Computer Science, Delft University of Technology, P.O. Box 5031, 2600 GA Delft, The Netherlands; [email protected]
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Abstract

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

Keywords

Semidefinite optimizationinterior-point methodsprimal-dual methodcomplexity.
Type
Research Article
Information
RAIRO - Operations Research , Volume 43 , Issue 2 , April 2009 , pp. 189 - 199
Copyright
© EDP Sciences, ROADEF, SMAI, 2009

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References

F. Alizadeh, Combinatorial optimization with interior point methods and semi-definite matrices. Ph.D. thesis, University of Minnesota, Minneapolis, Minnesota, USA (1991).
Alizadeh, F., Interior point methods in semidefinite programming with applications to combinatorial optimization. SIAM J. Optim. 5 (1995) 13–51. CrossRef
Bai, Y.Q., El Ghami, M. and Roos, C., A comparative study of kernel functions for primal-dual interior-point algorithms in linear optimization. SIAM J. Optim. 15 (2004) 101–128. CrossRef
E. de Klerk, Aspects of semidefinite programming, Applied Optimization 65. Kluwer Academic Publishers, Dordrecht, The Netherlands (2002).
M. El Ghami, New primal-dual interior-point methods based on kernel functions. Ph.D. thesis, TU Delft, The Netherlands (2005).
El Ghami, M. and Roos, C., Generic primal-dual interior point methods based on a new Kernel function. RAIRO-Oper. Res. 42 (2008) 199–213.
R.A. Horn and C.R. Johnson, Matrix analysis. Cambridge University Press, Cambridge, UK (1985).
Y.E. Nesterov and A.S. Nemirovskii, Interior point polynomial methods in convex programming: theory and algorithms. SIAM Publications, SIAM, Philadelphia, USA (1993).
J. Peng, C. Roos and T. Terlaky, Self-regularity, a new paradigm for primal-dual interior-point algorithms. Princeton University Press (2002).
W. Rudin, Principles of mathematical analysis. Mac-Graw Hill Book Company, New York (1978).
Sturm, J.F. and Zhang, S., Symmetric primal-dual path following algorithms for semidefinite programming. Appl. Num. Math. 29 (1999) 301–315. CrossRef
Wang, G.Q., Bai, Y.Q. and Roos, C., Primal-dual interior-point algorithms for semidefinite optimization based on a simple kernel function. J. Math. Model. Algorithms 4 (2005) 409–433. CrossRef