Positivity

, Volume 22, Issue 1, pp 39–57 | Cite as

On penalty method for equilibrium problems in lexicographic order

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Abstract

In this paper, we consider lexicographic vector equilibrium problems. We propose a penalty function method for solving such problems. We show that every penalty trajectory of the penalized lexicographic equilibrium problem tends to the solution of the original problem. Using the regularized gap function to obtain an error bound result for such penalized problems is given.

Keywords

Lexicographic order Equilibrium problem Penalty method Gap function Error bound 

Mathematics Subject Classification

47J20 49M37 90C30 

Notes

Acknowledgements

The authors wish to thank the anonymous referees for the careful reviews and valuable comments that helped us significantly improve the presentation of the paper. This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant Number 101.01-2017.18.

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© Springer International Publishing 2017

Authors and Affiliations

  1. 1.Department of Mathematics, Teacher CollegeCantho UniversityCanthoVietnam
  2. 2.Department of MathematicsCantho Technical and Economic CollegeCanthoVietnam
  3. 3.Department of MathematicsUniversity of Science, Vietnam National University Ho Chi Minh CityHo Chi Minh CityVietnam

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