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An Extragradient Method for Solving Variational Inequalities without Monotonicity

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Abstract

A new extragradient projection method, which does not require generalized monotonicity, is devised in this paper. In order to ensure its global convergence, we assume only that the Minty variational inequality has a solution. In particular, it applies to quasimonotone variational inequalities having a nontrivial solution.

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Acknowledgements

The authors would like to thank the referees for valuable suggestions. This work was partially supported by National Natural Science Foundation of China under Grant 11871359.

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Authors and Affiliations

  1. Department of Mathematics, Sichuan Normal University, Chengdu, Sichuan, China

    Ming Lei & Yiran He

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  1. Ming Lei
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  2. Yiran He
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Correspondence to Yiran He.

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Communicated by Evgeni Alekseevich Nurminski.

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Lei, M., He, Y. An Extragradient Method for Solving Variational Inequalities without Monotonicity. J Optim Theory Appl 188, 432–446 (2021). https://doi.org/10.1007/s10957-020-01791-x

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  • DOI: https://doi.org/10.1007/s10957-020-01791-x

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