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

RAIRO - Operations Research (2010)

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

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topEL 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

top- 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
- 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
- E.M. Cho, Log-barrier method for two-stagequadratic stochastic programming. Appl. Math. Comput.164 (2005) 45–69. Zbl1071.65083
- 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
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- 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). Zbl0745.90069
- J. Miao, 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.
- 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
- 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
- J. Peng, C. Roos and T. Terlaky, Self-Regularity: A New Paradigm for Primal-Dual Interior-Point Algorithms. Princeton University Press (2002). Zbl1136.90045
- 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). Zbl0863.65031

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