An efficient projection-type method for monotone variational inequalities in Hilbert spaces

Y. Shehu, X.-H. Li, Q.-L. Dong, Numerical Algorithms (2019) 1–24.

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Journal Article | Epub ahead of print | English
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Abstract
We consider the monotone variational inequality problem in a Hilbert space and describe a projection-type method with inertial terms under the following properties: (a) The method generates a strongly convergent iteration sequence; (b) The method requires, at each iteration, only one projection onto the feasible set and two evaluations of the operator; (c) The method is designed for variational inequality for which the underline operator is monotone and uniformly continuous; (d) The method includes an inertial term. The latter is also shown to speed up the convergence in our numerical results. A comparison with some related methods is given and indicates that the new method is promising.
Publishing Year
Date Published
2019-06-27
Journal Title
Numerical Algorithms
Page
1-24
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Shehu Y, Li X-H, Dong Q-L. An efficient projection-type method for monotone variational inequalities in Hilbert spaces. Numerical Algorithms. 2019:1-24. doi:10.1007/s11075-019-00758-y
Shehu, Y., Li, X.-H., & Dong, Q.-L. (2019). An efficient projection-type method for monotone variational inequalities in Hilbert spaces. Numerical Algorithms, 1–24. https://doi.org/10.1007/s11075-019-00758-y
Shehu, Yekini, Xiao-Huan Li, and Qiao-Li Dong. “An Efficient Projection-Type Method for Monotone Variational Inequalities in Hilbert Spaces.” Numerical Algorithms, 2019, 1–24. https://doi.org/10.1007/s11075-019-00758-y.
Y. Shehu, X.-H. Li, and Q.-L. Dong, “An efficient projection-type method for monotone variational inequalities in Hilbert spaces,” Numerical Algorithms, pp. 1–24, 2019.
Shehu Y, Li X-H, Dong Q-L. 2019. An efficient projection-type method for monotone variational inequalities in Hilbert spaces. Numerical Algorithms., 1–24.
Shehu, Yekini, et al. “An Efficient Projection-Type Method for Monotone Variational Inequalities in Hilbert Spaces.” Numerical Algorithms, Springer Nature, 2019, pp. 1–24, doi:10.1007/s11075-019-00758-y.
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