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A projection-like method for quasimonotone variational inequalities without Lipschitz continuity

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Abstract

For most projection methods, the operator of a variational inequality problem is assumed to be monotone (or pseudomonotone) and Lipschitz continuous. In this paper, we present a projection-like method to solve quasimonotone variational inequality problems without Lipschitz continuity. Under some mild assumptions, we prove that the sequence generated by the proposed algorithm converges to a solution. Numerical experiments are provided to show the effectiveness of the method.

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Acknowledgements

The authors would like to thank the referees and the editor, for their comments, which greatly improved the presentation of this paper.

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Authors and Affiliations

  1. Institute of Mathematics, University of würzburg, 97074, würzburg, Germany

    Xiaoxi Jia

  2. School of Mathematical Sciences, Jiangsu Key Laboratory for NSLSCS, Nanjing Normal University, Nanjing, 210023, China

    Lingling Xu

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  1. Xiaoxi Jia
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  2. Lingling Xu
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Correspondence to Lingling Xu.

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The work is supported by grant National Natural Science Foundation of China (NSFC) 11971238.

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Jia, X., Xu, L. A projection-like method for quasimonotone variational inequalities without Lipschitz continuity. Optim Lett 16, 2387–2403 (2022). https://doi.org/10.1007/s11590-022-01874-w

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  • DOI: https://doi.org/10.1007/s11590-022-01874-w

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