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An Extragradient Algorithm for Monotone Variational Inequalities

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Cybernetics and Systems Analysis Aims and scope

Abstract

A new iterative algorithm is proposed for solving the variational inequality problem with a monotone and Lipschitz continuous mapping in a Hilbert space. The algorithm is based on the following two well-known methods: the Popov algorithm and so-called subgradient extragradient algorithm. An advantage of the algorithm is the computation of only one value of the inequality mapping and one projection onto the admissible set per one iteration. The weak convergence of sequences generated by the proposed algorithm is proved.

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Authors and Affiliations

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

    Yu. V. Malitsky & V. V. Semenov

Authors
  1. Yu. V. Malitsky
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  2. V. V. Semenov
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Correspondence to Yu. V. Malitsky.

Additional information

This work was financed by the Verkhovna Rada of Ukraine (the nominal grant of the Verkhovna Rada of Ukraine for 2013 to support scientific researches of young scientists) and the State Fund for Fundamental Researches of Ukraine (project GP/F49/061).

Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 125–131, March–April, 2014.

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Malitsky, Y.V., Semenov, V.V. An Extragradient Algorithm for Monotone Variational Inequalities. Cybern Syst Anal 50, 271–277 (2014). https://doi.org/10.1007/s10559-014-9614-8

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  • DOI: https://doi.org/10.1007/s10559-014-9614-8

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