A subgradient algorithm for a class of nonlinear split feasibility problems: application to jointly constrained Nash equilibrium models

Abstract

In this paper we propose an algorithm for solving the split feasibility problem \(x\in C, Ax\in Q\) with C being the solution set of an equilibrium problem and A can be nonlinear. The proposed algorithm is a combination between the projection method for the equilibrium problem and the gradient method for the inclusion \(Ax\in Q\). The convergence of the algorithm is investigated. A numerical example for a jointly constrained Nash equilibrium model in electricity production market is provided to demonstrate the behavior of the algorithm.

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Acknowledgements

We would like to thank the editor and the referees very much for their useful comments, remarks and suggestions that helped us very much to improve quality of the paper. The first author would also like to thank the Vietnam Institute for Advanced Study in Mathematics (VIASM) for the support during her visit.

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Correspondence to Le Hai Yen.

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This paper is supported by the NAFOSTED, Grant 101.01-2017.315.

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Yen, L.H., Huyen, N.T.T. & Muu, L.D. A subgradient algorithm for a class of nonlinear split feasibility problems: application to jointly constrained Nash equilibrium models. J Glob Optim 73, 849–868 (2019). https://doi.org/10.1007/s10898-018-00735-0

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Keywords

  • Nonlinear split feasibility
  • Equilibria
  • Subgradient method
  • Quasiconvexity
  • Nash model