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Journal of Global Optimization

, Volume 64, Issue 1, pp 179–195 | Cite as

On ergodic algorithms for equilibrium problems

  • P. N. Anh
  • T. N. Hai
  • P. M. Tuan
Article

Abstract

In this paper, we present a new iteration method for solving monotone equilibrium problems. This new method is based on the ergodic iteration method Ronald and Bruck in (J Math Anal Appl 61:159–164, 1977) and the auxiliary problem principle Noor in (J Optim Theory Appl 122:371–386, 2004), but it includes the usage of symmetric and positive definite matrices. The proposed algorithm is very simple. Moreover, it simplifies the assumptions necessary in order to converge to the solution. Specifically, whereas previous methods require strong monotonicity and Lipschitz-type continuous conditions, our proposed method only requires weak monotonicity conditions. Applications to the generalized variational inequality problem and some numerical results are reported.

Keywords

Equilibrium problem Monotone Ergodic algorithm Auxiliary problem principle 

Mathematics Subject Classification

65 K10 90 C25 

Notes

Acknowledgments

We are grateful to the anonymous referees for their really helpful and constructive comments that helped us very much to improve the original version of the paper substantially.

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of Scientific FundamentalsPosts and Telecommunications Institute of TechnologyHanoiVietnam
  2. 2.School of Applied Mathematics and InformaticsHa Noi University of Science and TechnologyHanoiVietnam
  3. 3.Academy of Military Science and TechnologyHanoiVietnam

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