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

M. EL Ghami; T. Steihaug

RAIRO - Operations Research (2010)

  • Volume: 44, Issue: 3, page 185-205
  • ISSN: 0399-0559

Abstract

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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 the class of self-regular kernel functions. The class is defined by some simple conditions on the growth and the barrier behavior of the kernel function. In this paper we generalize the analysis presented in the above paper for P*(κ) Linear Complementarity Problems (LCPs). The analysis for LCPs deviates significantly from the analysis for linear optimization. Several new tools and techniques are derived in this paper.

How to cite

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EL Ghami, M., and Steihaug, T.. "Kernel-function Based Primal-Dual Algorithms for P*(κ) Linear Complementarity Problems." RAIRO - Operations Research 44.3 (2010): 185-205. <http://eudml.org/doc/250843>.

@article{ELGhami2010,
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 the class of self-regular kernel functions. The class is defined by some simple conditions on the growth and the barrier behavior of the kernel function. In this paper we generalize the analysis presented in the above paper for P*(κ) Linear Complementarity Problems (LCPs). The analysis for LCPs deviates significantly from the analysis for linear optimization. Several new tools and techniques are derived in this paper. },
author = {EL Ghami, M., Steihaug, T.},
journal = {RAIRO - Operations Research},
keywords = {Interior-point; central paths; Kernel functions; primal-dual method; large update; small update; linear complementarity problem; interior-point; small update},
language = {eng},
month = {7},
number = {3},
pages = {185-205},
publisher = {EDP Sciences},
title = {Kernel-function Based Primal-Dual Algorithms for P*(κ) Linear Complementarity Problems},
url = {http://eudml.org/doc/250843},
volume = {44},
year = {2010},
}

TY - JOUR
AU - EL Ghami, M.
AU - Steihaug, T.
TI - Kernel-function Based Primal-Dual Algorithms for P*(κ) Linear Complementarity Problems
JO - RAIRO - Operations Research
DA - 2010/7//
PB - EDP Sciences
VL - 44
IS - 3
SP - 185
EP - 205
AB - 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 the class of self-regular kernel functions. The class is defined by some simple conditions on the growth and the barrier behavior of the kernel function. In this paper we generalize the analysis presented in the above paper for P*(κ) Linear Complementarity Problems (LCPs). The analysis for LCPs deviates significantly from the analysis for linear optimization. Several new tools and techniques are derived in this paper.
LA - eng
KW - Interior-point; central paths; Kernel functions; primal-dual method; large update; small update; linear complementarity problem; interior-point; small update
UR - http://eudml.org/doc/250843
ER -

References

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  1. Y.Q. Bai, M. El Ghami and C. Roos, A new efficient large-update primal-dual interior-point method based on a finite barrier. SIAM J. Opt.13 (2003) 766–782.  Zbl1036.90051
  2. Y.Q. Bai, M. El Ghami and C. Roos, A comparative study of kernel functions for primal-dual interior-point algorithms in linear optimization. SIAM J. Opt.15 (2004) 101–128.  Zbl1077.90038
  3. E.M. Cho, Log-barrier method for two-stagequadratic stochastic programming. Appl. Math. Comput.164 (2005) 45–69.  Zbl1071.65083
  4. 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.  Zbl1108.65061
  5. R. Cottle, J.S. Pang and R.E. Stone, The Linear Complementarity Problem. Academic Press, Boston (1992).  Zbl0757.90078
  6. M. El Ghami, Y.Q. Bai and C. Roos, Kernel Function Based Algorithms for Semidefinite Optimization. Int. J. RAIRO-Oper. Res.43 (2009) 189–199.  Zbl1170.90455
  7. T. Illés and M. Nagy, The Mizuno-Todd-Ye predictor-corrector algorithm for sufficient matrix linear complementarity problem. Alkalmaz. Mat. Lapok22 (2005) 41–61.  Zbl1136.90485
  8. 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.  
  9. 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).  Zbl0745.90069
  10. J. Miao, A quadratically convergent o(1+k) n l -iteration algorithm for the P*(k)-matrix linear complementarity problem. Math. Program.69 (1995) 355–368.  
  11. R.D.C. Monteiro and I. Adler, Interior path following primal-dual algorithms. Part I: Linear programming. Math. Program.44 (1989) 27–41.  Zbl0676.90038
  12. J. Peng, C. Roos and T. Terlaky, Self-regular functions and new search directions for linear and semidefinite optimization. Math. Program.93 (2002) 129–171.  Zbl1007.90037
  13. J. Peng, C. Roos and T. Terlaky, Self-Regularity: A New Paradigm for Primal-Dual Interior-Point Algorithms. Princeton University Press (2002).  Zbl1136.90045
  14. C. Roos, T. Terlaky and J.-Ph. Vial, Theory and Algorithms for Linear Optimization. An Interior-Point Approach. Springer Science (2005).  
  15. S.J. Wright, Primal-Dual Interior-Point Methods. SIAM, Philadelphia, USA (1997).  Zbl0863.65031

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