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

Zeitschrift:: Numerical Algorithms > Ausgabe 1/2020

Autoren:: Yekini Shehu, Xiao-Huan Li, Qiao-Li Dong

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The research of this author is supported by the ERC grant at the IST.

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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.

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Titel: An efficient projection-type method for monotone variational inequalities in Hilbert spaces
Autoren:: Yekini Shehu
Xiao-Huan Li
Qiao-Li Dong
Publikationsdatum: 27.06.2019
DOI: https://doi.org/10.1007/s11075-019-00758-y
Verlag: Springer US
Zeitschrift: Numerical Algorithms
Ausgabe 1/2020
Print ISSN: 1017-1398
Elektronische ISSN: 1572-9265

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