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A self-adaptive method for pseudomonotone equilibrium problems and variational inequalities

  • Jun YangEmail author
  • Hongwei Liu
Article
  • 64 Downloads

Abstract

In this paper, we introduce and analyze a new algorithm for solving equilibrium problem involving pseudomonotone and Lipschitz-type bifunction in real Hilbert space. The algorithm requires only a strongly convex programming problem per iteration. A weak and a strong convergence theorem are established without the knowledge of the Lipschitz-type constants of the bifunction. As a special case of equilibrium problem, the variational inequality is also considered. Finally, numerical experiments are performed to illustrate the advantage of the proposed algorithm.

Keywords

Equilibrium problem Pseudomonotone bifunction Gradient method Variational inequality 

Mathematics Subject Classification

65J15 90C33 90C25 90C52 

Notes

Acknowledgements

The authors would like to thank the Associate Editor and the anonymous referees for their valuable comments and suggestions which helped to improve the original version of this paper.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsXidian UniversityXi’anChina
  2. 2.School of Mathematics and Information ScienceXianyang Normal UniversityXianyangChina

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