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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; [email protected]
Wilfredo Sosa
Affiliation:
Instituto de Matemática e Ciencias Afines – Universidad Nacional de Ingeniería, Jirón Ancash 536, Lima 1, Lima, Peru; [email protected]
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Abstract

We present a variant of the analytic center cutting plane algorithm proposedby Goffin et al. (1996) to approximately solve equilibrium problemsas proposed by Blum and Oettli (1994), which include as particular problemsthe variational inequalities problem, the Nash equilibria problem innon-cooperative games, the convex minimization problem, and the fixed pointproblem. Furthermore, we analyze the convergence and complexity of the modifiedalgorithm.

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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