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

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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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Discussion with Christian Kanzow is gratefully acknowledged.

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Correspondence to Yekini Shehu.

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

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Shehu, Y., Li, XH. & Dong, QL. An efficient projection-type method for monotone variational inequalities in Hilbert spaces. Numer Algor 84, 365–388 (2020). https://doi.org/10.1007/s11075-019-00758-y

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