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Kernel-function Based Primal-Dual Algorithms for P * (κ) Linear Complementarity Problems

Published online by Cambridge University Press:  23 July 2010

M. EL Ghami  and
T. Steihaug
M. EL Ghami
Affiliation:
Department of Informatics, University of Bergen, Post Box 7803, 5020 Bergen, Norway; melghami@ii.uib.no ; Trond.Steihaug@ii.uib.no
T. Steihaug
Affiliation:
Department of Informatics, University of Bergen, Post Box 7803, 5020 Bergen, Norway; melghami@ii.uib.no ; Trond.Steihaug@ii.uib.no
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Abstract

Recently, [Y.Q. Bai, M. El Ghami and C. Roos,SIAM J. Opt. 15 (2004) 101–128]investigated a new class of kernel functions which differs from theclass of self-regular kernel functions. The class is defined by somesimple conditions on the growth and the barrier behavior of thekernel function. In this paper we generalize theanalysis presented in the above paper for P * (κ) LinearComplementarity Problems (LCPs). The analysis for LCPs deviates significantly from the analysisfor linear optimization. Several new tools and techniques are derived in this paper.

Keywords

Interior-pointcentral pathsKernel functionsprimal-dual methodlarge updatesmall updatelinear complementarity problem

Information

Type
Research Article
Information
RAIRO - Operations Research , Volume 44 , Issue 3 , July 2010 , pp. 185 - 205
Copyright
© EDP Sciences, ROADEF, SMAI, 2010

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References

Bai, Y.Q., El Ghami, M. and Roos, C., A new efficient large-update primal-dual interior-point method based on a finite barrier. SIAM J. Opt. 13 (2003) 766–782. 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. Opt. 15 (2004) 101–128. CrossRef
Cho, E.M., Log-barrier method for two-stagequadratic stochastic programming. Appl. Math. Comput. 164 (2005) 45–69.
Gyeong-Mi Cho and Min-Kyung Kim, A new Large-update interior point algorithm for P * (κ) LCPs Based on kernel functions. Appl. Math. Comput. 182 (2006) 1169–1183.
R. Cottle, J.S. Pang and R.E. Stone, The Linear Complementarity Problem. Academic Press, Boston (1992).
El Ghami, M., Bai, Y.Q. and Roos, C., Kernel Function Based Algorithms for Semidefinite Optimization. Int. J. RAIRO-Oper. Res. 43 (2009) 189–199. CrossRef
Illés, T. and Nagy, M., The Mizuno-Todd-Ye predictor-corrector algorithm for sufficient matrix linear complementarity problem. Alkalmaz. Mat. Lapok 22 (2005) 41–61.
M. Kojima, N. Megiddo, T. Noma and A. Yoshise, A primal-dual interior point algorithm for linear programming, in: Progress in Mathematical Programming; Interior Point Related Methods, 10, edited by N. Megiddo. Springer Verlag, New York (1989) pp. 29–47.
M. Kojima, N. Megiddo, T. Noma and A. Yoshise, A unified approach to interior point algorithms for linear complementarity problems, Lect. Notes Comput. Sci. 538 (1991).
Miao, J., A quadratically convergent o(1+k) $\sqrt{n}l$ -iteration algorithm for the P * (k)-matrix linear complementarity problem. Math. Program. 69 (1995) 355–368.
Monteiro, R.D.C. and Adler, I., Interior path following primal-dual algorithms. Part I: Linear programming. Math. Program. 44 (1989) 27–41. CrossRef
Peng, J., Roos, C. and Terlaky, T., Self-regular functions and new search directions for linear and semidefinite optimization. Math. Program. 93 (2002) 129–171. CrossRef
J. Peng, C. Roos and T. Terlaky, Self-Regularity: A New Paradigm for Primal-Dual Interior-Point Algorithms. Princeton University Press (2002).
C. Roos, T. Terlaky and J.-Ph. Vial, Theory and Algorithms for Linear Optimization. An Interior-Point Approach. Springer Science (2005).
S.J. Wright, Primal-Dual Interior-Point Methods. SIAM, Philadelphia, USA (1997).