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New algorithms and convergence theorems for solving variational inequalities with non-Lipschitz mappings

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Abstract

We propose and study new projection-type algorithms for solving pseudomonotone variational inequality problems in real Hilbert spaces without assuming Lipschitz continuity of the cost operators. We prove weak and strong convergence theorems for the sequences generated by these new methods. The numerical behavior of the proposed algorithms when applied to several test problems is compared with that of several previously known algorithms.

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Acknowledgments

All the authors are grateful to an anonymous referee for several helpful comments and useful suggestions.

Funding

Simeon Reich was partially supported by the Israel Science Foundation (Grant 820/17), the Fund for the Promotion of Research at the Technion and by the Technion General Research Fund. Vu Tien Dung was partially supported by the National Foundation for Science and Technology Development under Grant 101.01-2019.320.

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Authors and Affiliations

  1. Department of Mathematics, The Technion – Israel Institute of Technology, 32000, Haifa, Israel

    Simeon Reich

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

    Duong Viet Thong

  3. Tianjin Key Laboratory for Advanced Signal Processing and College of Science, Civil Aviation University of China, Tianjin, 300300, China

    Qiao-Li Dong & Xiao-Huan Li

  4. Department of Mathematics, Vietnam National University, 334 Nguyen Trai, Thanh Xuan, Hanoi, Vietnam

    Vu Tien Dung

Authors
  1. Simeon Reich
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  2. Duong Viet Thong
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  3. Qiao-Li Dong
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  4. Xiao-Huan Li
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  5. Vu Tien Dung
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Correspondence to Duong Viet Thong.

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Reich, S., Thong, D.V., Dong, QL. et al. New algorithms and convergence theorems for solving variational inequalities with non-Lipschitz mappings. Numer Algor 87, 527–549 (2021). https://doi.org/10.1007/s11075-020-00977-8

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  • DOI: https://doi.org/10.1007/s11075-020-00977-8

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