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

  • Trinh Ngoc HaiEmail author
Original Paper
  • 45 Downloads

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.

Keywords

Variational inequality Complexity bound Equilibrium problem Strong pseudomonotonicity 

Notes

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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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Applied Mathematics and InformaticsHanoi University of Science and TechnologyHanoiVietnam

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