Convergence analysis of projection method for variational inequalities

Y. Shehu, O.S. Iyiola, X.-H. Li, Q.-L. Dong, Computational and Applied Mathematics 38 (2019) 161.

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Journal Article | Published | English
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Abstract
The main contributions of this paper are the proposition and the convergence analysis of a class of inertial projection-type algorithm for solving variational inequality problems in real Hilbert spaces where the underline operator is monotone and uniformly continuous. We carry out a unified analysis of the proposed method under very mild assumptions. In particular, weak convergence of the generated sequence is established and nonasymptotic O(1 / n) rate of convergence is established, where n denotes the iteration counter. We also present some experimental results to illustrate the profits gained by introducing the inertial extrapolation steps.
Publishing Year
Date Published
2019-10-04
Journal Title
Computational and Applied Mathematics
Volume
38
Issue
4
Article Number
161
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eISSN
IST-REx-ID

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Shehu Y, Iyiola OS, Li X-H, Dong Q-L. Convergence analysis of projection method for variational inequalities. Computational and Applied Mathematics. 2019;38(4):161. doi:10.1007/s40314-019-0955-9
Shehu, Y., Iyiola, O. S., Li, X.-H., & Dong, Q.-L. (2019). Convergence analysis of projection method for variational inequalities. Computational and Applied Mathematics, 38(4), 161. https://doi.org/10.1007/s40314-019-0955-9
Shehu, Yekini, Olaniyi S. Iyiola, Xiao-Huan Li, and Qiao-Li Dong. “Convergence Analysis of Projection Method for Variational Inequalities.” Computational and Applied Mathematics 38, no. 4 (2019): 161. https://doi.org/10.1007/s40314-019-0955-9.
Y. Shehu, O. S. Iyiola, X.-H. Li, and Q.-L. Dong, “Convergence analysis of projection method for variational inequalities,” Computational and Applied Mathematics, vol. 38, no. 4, p. 161, 2019.
Shehu Y, Iyiola OS, Li X-H, Dong Q-L. 2019. Convergence analysis of projection method for variational inequalities. Computational and Applied Mathematics. 38(4), 161.
Shehu, Yekini, et al. “Convergence Analysis of Projection Method for Variational Inequalities.” Computational and Applied Mathematics, vol. 38, no. 4, Springer Nature, 2019, p. 161, doi:10.1007/s40314-019-0955-9.

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