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An extragradient projection method for strongly quasiconvex equilibrium problems with applications

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Abstract

We discuss an extragradient projection method for dealing with equilibrium problems involving bifunctions which are strongly quasiconvex on its second argument. The algorithm combines a proximal step with a subgradient projection step using a generalized subdifferential, which is especially useful for dealing with this class of generalized convex functions, and with a line search. As a consequence, the usual assumption regarding the relationship between the Lipschitz-type parameter and the modulus of strong quasiconvexity is no longer needed for ensuring the convergence of the generated sequence to the solution of the problem. Furthermore, numerical experiments for classes of nonconvex mixed variational inequalities based on fractional programming problems are given in order to show the performance of our proposed method.

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Acknowledgements

Part of this work was carried out when F. Lara was visiting the Institute of Mathematics of the Vietnam Academy of Sciences and Technology (VAST), in Hanoi, Vietnam, during March 2023. This author wishes to thank the Institute for its hospitality. This research was partially supported by ANID–Chile under project Fondecyt Regular 1220379 (Lara) and by Vietnam Academy of Science and Technology under Grant Number CTTH00.02/24-25 (Yen).

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Authors and Affiliations

  1. Instituto de Alta Investigación (IAI), Universidad de Tarapacá, Arica, Chile

    F. Lara & R. T. Marcavillaca

  2. Institute of Mathematics, Vietnam Academy of Sciences and Technology (VAST), Hanoi, Vietnam

    L. H. Yen

Authors
  1. F. Lara
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  2. R. T. Marcavillaca
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  3. L. H. Yen
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Correspondence to F. Lara.

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Communicated by Gabriel Haeser.

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Lara, F., Marcavillaca, R.T. & Yen, L.H. An extragradient projection method for strongly quasiconvex equilibrium problems with applications. Comp. Appl. Math. 43, 128 (2024). https://doi.org/10.1007/s40314-024-02626-5

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  • DOI: https://doi.org/10.1007/s40314-024-02626-5

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