Abstract
We present Tseng's forward-backward-forward method with extrapolation from the past for pseudo-monotone variational inequalities in Hilbert spaces. In addition, we propose a variable stepsize scheme of the extrapolated Tseng's algorithm governed by the operator which is pseudo-monotone, Lipschitz continuous and sequentially weak-to-weak continuous. We also investigate the algorithm's adaptive stepsize scenario, which arises when it is impossible to calculate the Lipschitz constant of a pseudo-monotone operator correctly. Finally, we prove a weak convergence theorem and conduct a numerical experiment to support it.
Funding Statement
This work was supported by the Development and Promotion of Science and Technology Talents Project (DPST) scholarship, Royal Government of Thailand scholarship.
Acknowledgments
The author are very thankful to Dr. habil. Ernö Robert Csetnek for his careful guidance. The author wants to thank the guidance in programming from Dr. Phan Tu Vuong and the helpful comments from the referees.
Citation
Buris Tongnoi. "A Modified Tseng's Algorithm with Extrapolation from the Past for Pseudo-monotone Variational Inequalities." Taiwanese J. Math. 28 (1) 187 - 210, February, 2024. https://doi.org/10.11650/tjm/230906
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