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A hybrid method without extrapolation step for solving variational inequality problems

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Abstract

In this paper, we introduce a new method for solving variational inequality problems with monotone and Lipschitz-continuous mapping in Hilbert space. The iterative process is based on well-known projection method and the hybrid (or outer approximation) method. However we do not use an extrapolation step in the projection method. The absence of one projection in our method is explained by slightly different choice of sets in the hybrid method. We prove a strong convergence of the sequences generated by our method.

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Acknowledgments

The authors would like to extend their gratitude towards anonymous referees whose constructive suggestions helped us to improve the presentation of this paper.

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Authors and Affiliations

  1. Department of Cybernetics, Taras Shevchenko National University of Kyiv, 64/13, Volodymyrska Str., Kiev,  01601, Ukraine

    Yu. V. Malitsky & V. V. Semenov

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

Additional information

The research was partially supported by the Ukrainian State Fund for Fundamental Researches under Grants GP/F44/042, GP/F49/061.

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Malitsky, Y.V., Semenov, V.V. A hybrid method without extrapolation step for solving variational inequality problems. J Glob Optim 61, 193–202 (2015). https://doi.org/10.1007/s10898-014-0150-x

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