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An Armijo-type method for pseudomonotone equilibrium problems and its applications

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Abstract

We present a new algorithm for solving equilibrium problems, where the underlying bifunctions are pseudomonotone and not necessarily Lipschitz-type continuous. The algorithm is based on the auxiliary problem principle and the Armijo-type linesearch techniques. Convergence properties of the algorithms are established, among them the global convergence is proved under few assumptions. Applications to generalized variational inequalities and some numerical results are reported.

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Author notes

  1. P. N. Anh

    Present address: Laboratory of Theoretical and Applied Computer Science, LITA EA 3097, UFR MIM, University of Lorraine, Ile du Saulcy, 57045, Metz, France

Authors and Affiliations

  1. Department of Scientific Fundamentals, Posts and Telecommunications Institute of Technology, Hanoi, Vietnam

    P. N. Anh

  2. Laboratory of Theoretical and Applied Computer Science, LITA EA 3097, UFR MIM, University of Lorraine, Ile du Saulcy, 57045, Metz, France

    H. A. Le Thi

Authors
  1. P. N. Anh
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  2. H. A. Le Thi
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Corresponding author

Correspondence to H. A. Le Thi.

Additional information

This research has been suported by “Fonds Européens de Développement Régional” (FEDER) Lorraine, France.

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Anh, P.N., Le Thi, H.A. An Armijo-type method for pseudomonotone equilibrium problems and its applications. J Glob Optim 57, 803–820 (2013). https://doi.org/10.1007/s10898-012-9970-8

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  • DOI: https://doi.org/10.1007/s10898-012-9970-8

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