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A proximal method for equilibrium problems under growth conditions

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Abstract

Inspired by some growth conditions used in convex and nonconvex optimization and given a bifunction defined on a nonempty closed subset of a real Hilbert space, we design a Proximal Point Method for finding its equilibria points. Then, we investigate the convergence of this scheme under a regularity metric type assumption and state other metric regularity conditions. The purpose of this short article is mainly to launch new ideas and bring some novelty in this field.

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Acknowledgements

The first author wishes to thank Prof. M. Ouladsine, Head of the LSIS Team, for his confidence and support that allowed his transfer to Aix-Marseille University. The authors would also to thank the anonymous referees for their careful reading of the paper, for their comments and suggestions which improved the presentation of the present manuscript.

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Authors and Affiliations

  1. Aix Marseille Université, CNRS, LSIS UMR 7296, 13397, Marseille, France

    Abdellatif Moudafi

  2. Department of Mathematics, COMSATS, Institute of Information Technology, Islamabad, Pakistan

    Muhammad Aslam Noor

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  1. Abdellatif Moudafi
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  2. Muhammad Aslam Noor
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Correspondence to Abdellatif Moudafi.

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Moudafi, A., Noor, M.A. A proximal method for equilibrium problems under growth conditions. Afr. Mat. 28, 669–676 (2017). https://doi.org/10.1007/s13370-016-0474-4

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  • DOI: https://doi.org/10.1007/s13370-016-0474-4

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