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On gradient projection methods for strongly pseudomonotone variational inequalities without Lipschitz continuity

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Abstract

In this paper, we propose two new self-adaptive algorithms for solving strongly pseudomonotone variational inequalities. Our algorithms use dynamic step-sizes, chosen based on information of the previous step and their strong convergence is proved without the Lipschitz continuity of the underlying mappings. In contrast to the existing self-adaptive algorithms in Bello Cruz et al. (Comput Optim Appl 46:247–263, 2010), Santos et al. (Comput Appl Math 30:91–107, 2011), which use fast diminishing step-sizes, the new algorithms use arbitrarily slowly diminishing step sizes. This feature helps to speed up our algorithms. Moreover, we provide the worst case complexity bound of the proposed algorithms, which have not been done in the previous works. Some preliminary numerical experiences and comparisons are also reported.

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Acknowledgements

This research is funded by the Hanoi University of Science and Technology (HUST) under project number T2018-PC-121. The author thank two anonymous referees and the editor for their constructive comments which helped to improve the paper.

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  1. School of Applied Mathematics and Informatics, Hanoi University of Science and Technology, 1 Dai Co Viet, Hai Ba Trung, Hanoi, Vietnam

    Trinh Ngoc Hai

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  1. Trinh Ngoc Hai
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Correspondence to Trinh Ngoc Hai.

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Dedicated to Professor Pham Ky Anh on the Occasion of his 70th Birthday

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Hai, T.N. On gradient projection methods for strongly pseudomonotone variational inequalities without Lipschitz continuity. Optim Lett 14, 1177–1191 (2020). https://doi.org/10.1007/s11590-019-01424-x

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