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A New Non-Euclidean Proximal Method for Equilibrium Problems

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Recent Developments in Data Science and Intelligent Analysis of Information (ICDSIAI 2018)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 836))

Abstract

The paper analyzes the convergence of a new iterative algorithm for approximating solutions of equilibrium problems in finite-dimensional real vector space. Using the Bregman distance instead of the Euclidean, we modified the recently proposed two-stage proximal algorithm. The Bregman distance allows us to take into account the geometry of an admissible set effectively in some important cases. Namely, with the suitable choice of distance, we obtain a method with explicitly solvable auxiliary problems on the iterative steps. The convergence of the algorithm is proved under the assumption that the solution exists and the bifunction is pseudo-monotone and Lipschitz-type.

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Author information

Authors and Affiliations

  1. Infrastructure and Technologies State University, Kyiv, Ukraine

    Lyubov Chabak

  2. Faculty of Computer Sciences and Cybernetics, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

    Vladimir Semenov & Yana Vedel

Authors
  1. Lyubov Chabak
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  2. Vladimir Semenov
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  3. Yana Vedel
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Corresponding author

Correspondence to Vladimir Semenov .

Editor information

Editors and Affiliations

  1. Applied Mathematics Department, Igor Sikorsky Kyiv Polytechnic Institute, Kyiv, Ukraine

    Oleg Chertov

  2. Department of Economics, University of Pittsburgh, Pittsburgh, Pennsylvania, USA

    Tymofiy Mylovanov

  3. Department of Intelligent Information Systems, Petro Mohyla Black Sea National University, Mykolaiv, Ukraine

    Yuriy Kondratenko

  4. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Janusz Kacprzyk

  5. Department of Computer Science, University of Texas at El Paso, El Paso, Texas, USA

    Vladik Kreinovich

  6. Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia

    Vadim Stefanuk

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Chabak, L., Semenov, V., Vedel, Y. (2019). A New Non-Euclidean Proximal Method for Equilibrium Problems. In: Chertov, O., Mylovanov, T., Kondratenko, Y., Kacprzyk, J., Kreinovich, V., Stefanuk, V. (eds) Recent Developments in Data Science and Intelligent Analysis of Information. ICDSIAI 2018. Advances in Intelligent Systems and Computing, vol 836. Springer, Cham. https://doi.org/10.1007/978-3-319-97885-7_6

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