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Error bounds for strongly monotone and Lipschitz continuous variational inequalities

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Abstract

Our aim is to establish lower and upper error bounds for strongly monotone variational inequalities satisfying the Lipschitz continuity. In univariate case, the latter is not needed for getting an upper error bound and a lower error bound is proved by solely using the Lipschitz continuity.

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Acknowledgements

This research is funded by Vietnam National Foundation for Science and Technology (NAFOSTED) under grant 101.01-2017.325. The authors would like to thank Prof. Nguyen Dong Yen for helpful discussions on the subject. The detailed comments and suggestions of the two anonymous referees are gratefully acknowledged.

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Authors and Affiliations

  1. Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Khanh Duy Pham

  2. Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Khanh Duy Pham

  3. Department of Mathematics, University of British Columbia, Kelowna, BC, V1V 1V7, Canada

    Nhut Minh Bui

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  1. Khanh Duy Pham
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  2. Nhut Minh Bui
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Correspondence to Khanh Duy Pham.

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Pham, K.D., Bui, N.M. Error bounds for strongly monotone and Lipschitz continuous variational inequalities. Optim Lett 12, 971–984 (2018). https://doi.org/10.1007/s11590-017-1185-y

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  • DOI: https://doi.org/10.1007/s11590-017-1185-y

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