Iterative Methods for Triple Hierarchical Variational Inequalities in Hilbert Spaces

Iterative Methods for Triple Hierarchical Variational Inequalities in Hilbert Spaces

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Article ID: iaor201111153
Volume: 151
Issue: 3
Start Page Number: 489
End Page Number: 512
Publication Date: Dec 2011
Journal: Journal of Optimization Theory and Applications
Authors: , ,
Keywords: hierarchical structure, Hilbert space
Abstract:

In this paper, we consider a variational inequality with a variational inequality constraint over a set of fixed points of a nonexpansive mapping called triple hierarchical variational inequality. We propose two iterative methods, one is implicit and another one is explicit, to compute the approximate solutions of our problem. We present an example of our problem. The convergence analysis of the sequences generated by the proposed methods is also studied.

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