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Relaxed-Inertial Proximal Point Algorithms for Nonconvex Equilibrium Problems with Applications

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Abstract

We propose a relaxed-inertial proximal point algorithm for solving equilibrium problems involving bifunctions which satisfy in the second variable a generalized convexity notion called strong quasiconvexity, introduced by Polyak (Sov Math Dokl 7:72–75, 1966). The method is suitable for solving mixed variational inequalities and inverse mixed variational inequalities involving strongly quasiconvex functions, as these can be written as special cases of equilibrium problems. Numerical experiments where the performance of the proposed algorithm outperforms one of the standard proximal point methods are provided, too.

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Data Availability

No data sets were generated during the current study. The used matlab codes are available from all authors on reasonable request.

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Funding

The authors would like to thank the MATH AmSud cooperation program (Project AMSUD-220020) for its support. This research was partially supported by Anid–Chile under project Fondecyt Regular 1220379 (Lara), and by a CIAS Senior Research Fellow Grant of the Corvinus Institute for Advanced Studies, by the Hi! PARIS Center and by a public grant from the Fondation Mathématique Jacques Hadamard as part of the Investissement d’avenir project, reference ANR-11-LABX-0056-LMH, LabEx LMH (Grad).

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Authors and Affiliations

  1. Unité de Mathématiques Appliquées, ENSTA Paris, Institut Polytechnique de Paris, 91120, Palaiseau, France

    Sorin-Mihai Grad

  2. Instituto de Alta investigación (IAI), Universidad de Tarapacá, Arica, Chile

    Felipe Lara & Raúl Tintaya Marcavillaca

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  1. Sorin-Mihai Grad
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  2. Felipe Lara
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  3. Raúl Tintaya Marcavillaca
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All authors contributed equally to the study conception, design and implementation and wrote and corrected the manuscript.

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Correspondence to Felipe Lara.

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Communicated by Alexander Vladimirovich Gasnikov.

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Grad, SM., Lara, F. & Tintaya Marcavillaca, R. Relaxed-Inertial Proximal Point Algorithms for Nonconvex Equilibrium Problems with Applications. J Optim Theory Appl (2024). https://doi.org/10.1007/s10957-023-02375-1

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