On New Proximal Point Methods for Solving the Variational Inequalities

It is well known that the variational inequalities are equivalent to the fixed point problem. We use this alternative equivalent formulation to suggest and analyze some new proximal point methods for solving the variational inequalities. These new methods include the explicit, the implicit, and the...

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Bibliographic Details
Published in:Journal of Applied Mathematics 2012-01, Vol.2012 (2012), p.1334-1340-295
Main Authors: Aslam Noor, Muhammad, al-Said, Eisa A., Noor, Khalida Inayat
Format: Article
Language:English
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Summary:It is well known that the variational inequalities are equivalent to the fixed point problem. We use this alternative equivalent formulation to suggest and analyze some new proximal point methods for solving the variational inequalities. These new methods include the explicit, the implicit, and the extragradient methods as special cases. The convergence analysis of the new methods is considered under some suitable conditions. Results proved in this paper may stimulate further research in this direction.
ISSN:1110-757X
1687-0042
DOI:10.1155/2012/412413