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Computational Errors of the Extragradient Method for Equilibrium Problems

  • Pham Ngoc Anh
  • Nguyen Duc Hien
  • Pham Minh Tuan
Article

Abstract

Our aim in this paper is to study variants and computational errors of the extragradient method for solving equilibrium problems. First, we consider convergence of the method when domains in the auxiliary subproblems of the extragradient algorithm are replaced by outer and inner approximation polyhedra. Then, computational errors are showed under the asymptotic optimality condition, but the bifunction must satisfy certain Lipschitz-type continuous conditions. Next, by using Armijo-type linesearch techniques commonly used in variational inequalities, we obtain an approximation linesearch algorithm without Lipschitz continuity. Convergence analysis of the algorithms is considered under mild conditions on the iterative parameters.

Keywords

Equilibrium problems Semicontinuous Extragradient algorithm Computational errors 

Mathematics Subject Classification

65 K10 90 C25 47 H05 47 H09 

Notes

Acknowledgements

We are very grateful to the editor and anonymous referees for their comments that helped us very much in improving the paper. This research is funded by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant Number 101.02-2017.15.

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Copyright information

© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2018

Authors and Affiliations

  • Pham Ngoc Anh
    • 1
  • Nguyen Duc Hien
    • 2
  • Pham Minh Tuan
    • 3
  1. 1.Department of Scientific FundamentalsPosts and Telecommunications Institute of TechnologyHanoiVietnam
  2. 2.Office of Scientific Research and TechnologyDuy Tan UniversityDa NangVietnam
  3. 3.Academy of Military Science and TechnologyHanoiVietnam

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