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A generalized extragradient method for variational inequalities of the second kind

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Abstract

We formulate and analyze a generalized extragradient method for the iterative solution of variational inequalities of the second kind of the form \(f(u)+\partial \phi (u)\ni 0\), where f is a monotone Lipschitz continuous function and \(\phi :H\mapsto (-\infty ,\infty ]\) is a proper lower semi-continuous convex function defined on a Hilbert space. An illustrative example is included in the paper.

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Acknowledgements

The author is grateful to the anonymous referees for their suggestions which improved the content and presentation of the paper.

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  1. Department of Mathematics, Georgia Gwinnett College, Lawrenceville, USA

    Livinus U. Uko

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  1. Livinus U. Uko
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Correspondence to Livinus U. Uko.

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The code used for the illustrative example was written in Scilab, and is available to the reviewers upon request.

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Communicated by Orizon Pereira Ferreira.

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Uko, L.U. A generalized extragradient method for variational inequalities of the second kind. Comp. Appl. Math. 43, 2 (2024). https://doi.org/10.1007/s40314-023-02499-0

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