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Adaptive Extraproximal Algorithm for the Equilibrium Problem in Hadamard Spaces

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Optimization and Applications (OPTIMA 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12422))

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Abstract

In this paper, we consider equilibrium problems in Hadamard metric spaces. For an approximate solution of problems, a new iterative adaptive extra-proximal algorithm is proposed and studied. In contrast to the previously used rules for choosing the step size, the proposed algorithm does not calculate bifunction values at additional points and does not require knowledge of information on of bifunction’s Lipschitz constants. For pseudo-monotone bifunctions of Lipschitz type, the theorem on weak convergence of sequences generated by the algorithm is proved. The proof is based on the use of the Fejer property of the algorithm with respect to the set of solutions of problem. It is shown that the proposed algorithm is applicable to pseudo-monotone variational inequalities in Hilbert spaces.

This work was supported by the Ministry of Education and Science of Ukraine (project “Mathematical Modeling and Optimization of Dynamical Systems for Defense, Medicine and Ecology”, 0219U008403).

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Authors and Affiliations

  1. Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

    Yana Vedel & Vladimir Semenov

Authors
  1. Yana Vedel
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  2. Vladimir Semenov
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Correspondence to Yana Vedel .

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Editors and Affiliations

  1. Dorodnicyn Computing Centre, FRC CSC RAS, Moscow, Russia

    Nicholas Olenev

  2. Dorodnicyn Computing Centre, FRC CSC RAS, Moscow, Russia

    Yuri Evtushenko

  3. Krasovsky Institute of Mathematics and Mechanics, Ekaterinburg, Russia

    Michael Khachay

  4. Dorodnicyn Computing Centre, FRC CSC RAS, Moscow, Russia

    Vlasta Malkova

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Vedel, Y., Semenov, V. (2020). Adaptive Extraproximal Algorithm for the Equilibrium Problem in Hadamard Spaces. In: Olenev, N., Evtushenko, Y., Khachay, M., Malkova, V. (eds) Optimization and Applications. OPTIMA 2020. Lecture Notes in Computer Science(), vol 12422. Springer, Cham. https://doi.org/10.1007/978-3-030-62867-3_21

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