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Zbl 1235.65068
Noor, Muhammad Aslam; Noor, Khalida Inayat; Al-Said, Eisa
On new proximal point methods for solving the variational inequalities. (English)
[J] J. Appl. Math. 2012, Article ID 412413, 7 p. (2012). ISSN 1110-757X; ISSN 1687-0042/e

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.

MSC 2000:: *65K05 Mathematical programming (numerical methods)
49J40 Variational methods including variational inequalities
90C33 Complementarity problems

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