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An analytic center cutting plane algorithm for finding equilibrium points

Published online by Cambridge University Press:  01 July 2006

Fernanda M.P. Raupp  and
Wilfredo Sosa
Fernanda M.P. Raupp
Affiliation:
Laboratório Nacional de Computação Científica – MCT, Av. Getúlio Vargas, 333, Petrópolis, RJ, CEP 25651-075, Brazil; fernanda@lncc.br
Wilfredo Sosa
Affiliation:
Instituto de Matemática e Ciencias Afines – Universidad Nacional de Ingeniería, Jirón Ancash 536, Lima 1, Lima, Peru; sosa@uni.edu.pe
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Abstract

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.

Keywords

Equilibrium problemsconvex feasibility problemanalytic center cutting plane algorithm.
Type
Research Article
Information
RAIRO - Operations Research , Volume 40 , Issue 1 , January 2006 , pp. 37 - 52
Copyright
© EDP Sciences, 2006

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