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Mathematical Methods of Operations Research

, Volume 88, Issue 3, pp 399–415 | Cite as

An inertial-like proximal algorithm for equilibrium problems

  • Dang Van Hieu
Original Article

Abstract

The paper concerns with an inertial-like algorithm for approximating solutions of equilibrium problems in Hilbert spaces. The algorithm is a combination around the relaxed proximal point method, inertial effect and the Krasnoselski–Mann iteration. The using of the proximal point method with relaxations has allowed us a more flexibility in practical computations. The inertial extrapolation term incorporated in the resulting algorithm is intended to speed up convergence properties. The main convergence result is established under mild conditions imposed on bifunctions and control parameters. Several numerical examples are implemented to support the established convergence result and also to show the computational advantage of our proposed algorithm over other well known algorithms.

Keywords

Proximal point algorithm Inertial-like algorithm Monotone bifunction 

Mathematics Subject Classification

65J15 47H05 47J25 47J20 91B50 

Notes

Acknowledgements

The author would like to thank the Associate Editor and two anonymous referees for their valuable comments and suggestions which helped us very much in improving the original version of this paper.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Applied Analysis Research Group, Faculty of Mathematics and StatisticsTon Duc Thang UniversityHo Chi Minh CityVietnam

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