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Some proximal methods for solving mixed variational inequalities. (English) Zbl 1242.49018

Summary: It is well known that the mixed variational inequalities are equivalent to the fixed point problem. We use this alternative equivalent formulation to suggest some new proximal point methods for solving the mixed variational inequalities. These new methods include the explicit, the implicit, and the extragradient method as special cases. The convergence analysis of these new methods is considered under some suitable conditions. Our method of constructing these iterative methods is very simple. Results proved in this paper may stimulate further research in this direction.

MSC:

49J40 Variational inequalities
90C31 Sensitivity, stability, parametric optimization

References:

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