no. 3
Kernel-function based primal-dual algorithms for P*(κ) linear complementarity problems
RAIRO - Operations Research - Recherche Opérationnelle, Tome 44 (2010) no. 3, pp. 185-205.

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.

DOI : 10.1051/ro/2010014
Classification : 65K05, 90C33
Mots clés : interior-point, central paths, kernel functions, primal-dual method, large update, small update, linear complementarity problem 
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     author = {EL Ghami, M. and Steihaug, T.},
     title = {Kernel-function based primal-dual algorithms for $P*(\kappa )$ linear complementarity problems},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {185--205},
     publisher = {EDP-Sciences},
     volume = {44},
     number = {3},
     year = {2010},
     doi = {10.1051/ro/2010014},
     mrnumber = {2762793},
     zbl = {1206.90191},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1051/ro/2010014/}
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EL Ghami, M.; Steihaug, T. Kernel-function based primal-dual algorithms for $P*(\kappa )$ linear complementarity problems. RAIRO - Operations Research - Recherche Opérationnelle, Tome 44 (2010) no. 3, pp. 185-205. doi : 10.1051/ro/2010014. http://archive.numdam.org/articles/10.1051/ro/2010014/

[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. | Zbl

[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. | Zbl

[3] E.M. Cho, Log-barrier method for two-stagequadratic stochastic programming. Appl. Math. Comput. 164 (2005) 45-69. | Zbl

[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. | Zbl

[5] R. Cottle, J.S. Pang and R.E. Stone, The Linear Complementarity Problem. Academic Press, Boston (1992). | Zbl

[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. | EuDML | Numdam | Zbl

[7] T. Illés and M. Nagy, The Mizuno-Todd-Ye predictor-corrector algorithm for sufficient matrix linear complementarity problem. Alkalmaz. Mat. Lapok 22 (2005) 41-61. | Zbl

[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. | Zbl

[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). | Zbl

[10] J. Miao, A quadratically convergent o(1+k)nl-iteration algorithm for the P*(k)-matrix linear complementarity problem. Math. Program. 69 (1995) 355-368. | Zbl

[11] R.D.C. Monteiro and I. Adler, Interior path following primal-dual algorithms. Part I: Linear programming. Math. Program. 44 (1989) 27-41. | Zbl

[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. | Zbl

[13] J. Peng, C. Roos and T. Terlaky, Self-Regularity: A New Paradigm for Primal-Dual Interior-Point Algorithms. Princeton University Press (2002). | Zbl

[14] C. Roos, T. Terlaky and J.-Ph. Vial, Theory and Algorithms for Linear Optimization. An Interior-Point Approach. Springer Science (2005). | Zbl

[15] S.J. Wright, Primal-Dual Interior-Point Methods. SIAM, Philadelphia, USA (1997). | Zbl

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