Abstract
This paper investigates some inertial projection and contraction methods for solving pseudomonotone variational inequality problems in real Hilbert spaces. The algorithms use a new non-monotonic step size so that they can work without the prior knowledge of the Lipschitz constant of the operator. Strong convergence theorems of the suggested algorithms are obtained under some suitable conditions. Some numerical experiments in finite- and infinite-dimensional spaces and applications in optimal control problems are implemented to demonstrate the performance of the suggested schemes and we also compare them with several related results.
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Acknowledgements
The authors are very grateful to the editors and reviewers for their valuable and constructive comments that greatly improved the readability and quality of the initial version of the manuscript. This paper was supported by the National Natural Science Foundation of China under Grant No. 11401152.
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Tan, B., Qin, X. & Yao, JC. Strong convergence of inertial projection and contraction methods for pseudomonotone variational inequalities with applications to optimal control problems. J Glob Optim 82, 523–557 (2022). https://doi.org/10.1007/s10898-021-01095-y
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DOI: https://doi.org/10.1007/s10898-021-01095-y
Keywords
- Variational inequality problem
- Projection and contraction method
- Subgradient extragradient method
- Inertial method
- Pseudomonotone mapping
- Optimal control problem