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

Y. Shehu, X.-H. Li, Q.-L. Dong, Numerical Algorithms 84 (2020) 365–388.

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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
2020-05-01
Journal Title
Numerical Algorithms
Volume
84
Page
365-388
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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. 2020;84:365-388. doi:10.1007/s11075-019-00758-y
Shehu, Y., Li, X.-H., & Dong, Q.-L. (2020). An efficient projection-type method for monotone variational inequalities in Hilbert spaces. Numerical Algorithms, 84, 365–388. 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 84 (2020): 365–88. 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, vol. 84, pp. 365–388, 2020.
Shehu Y, Li X-H, Dong Q-L. 2020. An efficient projection-type method for monotone variational inequalities in Hilbert spaces. Numerical Algorithms. 84, 365–388.
Shehu, Yekini, et al. “An Efficient Projection-Type Method for Monotone Variational Inequalities in Hilbert Spaces.” Numerical Algorithms, vol. 84, Springer Nature, 2020, pp. 365–88, doi:10.1007/s11075-019-00758-y.
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