Abstract
A modified projection method for strongly pseudomonotone variational inequalities is considered. Strong convergence and error estimates for the sequences generated by this method are studied in two versions of the method: the stepsizes are chosen arbitrarily from a given fixed closed interval and the stepsizes form a non-summable decreasing sequence of positive real numbers. We also propose some interesting examples to analyze the obtained results.
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Acknowledgments
The research of the first author is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.02-2011.01. The second author is supported in part by Institute for Computational Science and Technology at Ho Chi Minh City (ICST HCMC), Vietnam and University of Technical Education Ho Chi Minh City. The authors would like to thank Prof. Van Hien Nguyen, Prof. Nguyen Dong Yen, and the two anonymous referees for valuable remarks and suggestions.
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Khanh, P.D., Vuong, P.T. Modified projection method for strongly pseudomonotone variational inequalities. J Glob Optim 58, 341–350 (2014). https://doi.org/10.1007/s10898-013-0042-5
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DOI: https://doi.org/10.1007/s10898-013-0042-5
Keywords
- Variational inequality
- Strong monotonicity
- Strong pseudomonotonicity
- Projection method
- Variable stepsizes
- Strong convergence
- Error estimates