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

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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.

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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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Authors and Affiliations

  1. School of Mathematics and Statistics, Xidian University, Xi’an, 710126, Shaanxi, China

    Jun Yang & Hongwei Liu

  2. School of Mathematics and Information Science, Xianyang Normal University, Xianyang, 712000, Shaanxi, China

    Jun Yang

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  1. Jun Yang
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  2. Hongwei Liu
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Correspondence to Jun Yang.

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Yang, J., Liu, H. A self-adaptive method for pseudomonotone equilibrium problems and variational inequalities . Comput Optim Appl 75, 423–440 (2020). https://doi.org/10.1007/s10589-019-00156-z

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  • DOI: https://doi.org/10.1007/s10589-019-00156-z

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