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We present a variant of the analytic center cutting plane algorithm proposed by Goffin et al. (1996) to approximately solve equilibrium problems as proposed by Blum and Oettli (1994), which include as particular problems the variational inequalities problem, the Nash equilibria problem in non-cooperative games, the convex minimization problem, and the fixed point problem. Furthermore, we analyze the convergence and complexity of the modified algorithm.
@article{RO_2006__40_1_37_0,
author = {Raupp, Fernanda M. P. and Sosa, Wilfredo},
title = {An analytic center cutting plane algorithm for finding equilibrium points},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {37--52},
publisher = {EDP-Sciences},
volume = {40},
number = {1},
year = {2006},
doi = {10.1051/ro:2006008},
mrnumber = {2248421},
zbl = {1198.90320},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/ro:2006008/}
}
TY - JOUR AU - Raupp, Fernanda M. P. AU - Sosa, Wilfredo TI - An analytic center cutting plane algorithm for finding equilibrium points JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2006 SP - 37 EP - 52 VL - 40 IS - 1 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/ro:2006008/ DO - 10.1051/ro:2006008 LA - en ID - RO_2006__40_1_37_0 ER -
%0 Journal Article %A Raupp, Fernanda M. P. %A Sosa, Wilfredo %T An analytic center cutting plane algorithm for finding equilibrium points %J RAIRO - Operations Research - Recherche Opérationnelle %D 2006 %P 37-52 %V 40 %N 1 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/ro:2006008/ %R 10.1051/ro:2006008 %G en %F RO_2006__40_1_37_0
Raupp, Fernanda M. P.; Sosa, Wilfredo. An analytic center cutting plane algorithm for finding equilibrium points. RAIRO - Operations Research - Recherche Opérationnelle, Tome 40 (2006) no. 1, pp. 37-52. doi: 10.1051/ro:2006008
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