Finite convergence of extragradient-type methods for solving variational inequalities under weak sharp condition

Trinh, Thanh Quoc, Vinh, Le Van and Vuong, Phan Tu (2022) Finite convergence of extragradient-type methods for solving variational inequalities under weak sharp condition. Computational and Applied Mathematics, 41 (8), [400]. (doi:10.1007/s40314-022-02110-y).

Record type: Article

Abstract

We prove the finite convergence of the sequences generated by some extragradient-type methods solving variational inequalities under the weakly sharp condition of the solution set. In addition, we provide estimations for the number of iterations to guarantee the sequence converges to a point in the solution set and prove that these estimations are optimal. Numerical examples are presented to illustrate the theoretical results.

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Accepted/In Press date: 3 November 2022

e-pub ahead of print date: 19 November 2022

Published date: 1 December 2022

Additional Information: Funding Information: The first and the second authors would like to thank Van Lang University, Vietnam for funding this work. The authors would like to thank referees for highly valuable comments and suggestions to help us improving the presentation of this paper. Publisher Copyright: © 2022, The Author(s).

Keywords: Finite convergence, Projection method, Variational inequality, Weak sharpness

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