Iterative methods for solving a class of monotone variational inequality problems with applications

In this paper, we provide a more general regularization method for seeking a solution to a class of monotone variational inequalities in a real Hilbert space, where the regularizer is a hemicontinuous and strongly monotone operator. As a discretization of the regularization method, we propose an ite...

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Bibliographic Details
Published in:Journal of inequalities and applications Vol. 2015; no. 1; pp. 1 - 17
Main Authors: Zhou, Haiyun, Zhou, Yu, Feng, Guanghui
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 24.02.2015
Springer Nature B.V
Subjects:
Analysis
Applications of Mathematics
Discretization
Inequalities
Iterative methods
Mapping
Mathematics
Mathematics and Statistics
Minimization
Norms
Operators
Optimization
Recent Advances in Inequalities and Applications from Real and Complex Analysis
Regularization
minimum-norm solution
47J20
41A65
Hilbert space
monotone variational inequality problem
iterative method
47H17
strong convergence
ISSN:1029-242X, 1025-5834, 1029-242X
Online Access:Get full text
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Summary:In this paper, we provide a more general regularization method for seeking a solution to a class of monotone variational inequalities in a real Hilbert space, where the regularizer is a hemicontinuous and strongly monotone operator. As a discretization of the regularization method, we propose an iterative method. We then prove that the proposed iterative method converges in norm to a solution of the class of monotone variational inequalities. We also apply our results to the constrained minimization problem and the minimum-norm fixed point problem for a generalized Lipschitz continuous and pseudocontractive mapping. The results presented in the paper improve and extend recent ones in the literature.
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ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-015-0590-y