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A New Two-Step Proximal Algorithm of Solving the Problem of Equilibrium Programming

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Optimization and Its Applications in Control and Data Sciences

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 115))

Abstract

We propose a new iterative two-step proximal algorithm for solving the problem of equilibrium programming in a Hilbert space. This method is a result of extension of L.D. Popov’s modification of Arrow-Hurwicz scheme for approximation of saddle points of convex-concave functions. The convergence of the algorithm is proved under the assumption that the solution exists and the bifunction is pseudo-monotone and Lipschitz-type.

Dedicated to Boris Polyak on the occasion of his 80th Birthday

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Acknowledgements

We are grateful to Yura Malitsky, Yana Vedel for discussions. We are very grateful to the referees for their really helpful and constructive comments. Vladimir Semenov thanks the State Fund for Fundamental Researches of Ukraine for support.

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Authors and Affiliations

  1. Department of Computational Mathematics, Kiev National Taras Shevchenko University, 64, Vladimirskaya Str., Kiev, 01601, Ukraine

    Sergey I. Lyashko & Vladimir V. Semenov

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  1. Sergey I. Lyashko
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  2. Vladimir V. Semenov
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Correspondence to Vladimir V. Semenov .

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Editors and Affiliations

  1. Department of Industrial and Systems Engineering, Ohio University, Athens, Ohio, USA

    Boris Goldengorin

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Lyashko, S.I., Semenov, V.V. (2016). A New Two-Step Proximal Algorithm of Solving the Problem of Equilibrium Programming. In: Goldengorin, B. (eds) Optimization and Its Applications in Control and Data Sciences. Springer Optimization and Its Applications, vol 115. Springer, Cham. https://doi.org/10.1007/978-3-319-42056-1_10

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