Strong convergence result for solving monotone variational inequalities in Hilbert space

In this paper, we study strong convergence of the algorithm for solving classical variational inequalities problem with Lipschitz-continuous and monotone mapping in real Hilbert space. The algorithm is inspired by Tseng’s extragradient method and the viscosity method with a simple step size. A stron...

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Bibliographic Details
Published in:Numerical algorithms Vol. 80; no. 3; pp. 741 - 752
Main Authors: Yang, Jun, Liu, Hongwei
Format: Journal Article
Language:English
Published: New York Springer US 01.03.2019
Springer Nature B.V
Subjects:
Algebra
Algorithms
Computer Science
Convergence
Hilbert space
Inequalities
Mapping
Mathematics
Numeric Computing
Numerical Analysis
Original Paper
Theory of Computation
Viscosity
Convex set
47J20
90C30
90C52
Monotone mapping
90C25
Projection
Extragradient method
Variational inequalities
ISSN:1017-1398, 1572-9265
Online Access:Get full text
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Summary:In this paper, we study strong convergence of the algorithm for solving classical variational inequalities problem with Lipschitz-continuous and monotone mapping in real Hilbert space. The algorithm is inspired by Tseng’s extragradient method and the viscosity method with a simple step size. A strong convergence theorem for our algorithm is proved without any requirement of additional projections and the knowledge of the Lipschitz constant of the mapping. Finally, we provide some numerical experiments to show the efficiency and advantage of the proposed algorithm.
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ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-018-0504-4