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An inexact hybrid projection-proximal point algorithm for solving generalized mixed variational inequalities. (English) Zbl 1236.49023
Summary: We investigate an inexact hybrid projection-proximal method for solving a class of generalized mixed variational inequalities in Hilbert spaces. We construct a general inexact hybrid projection-proximal point algorithm, in which an inexact relaxed proximal point step is followed by a suitable orthogonal projection onto a hyperplane. Under some suitable conditions concerned with the pseudomonotone set-valued mapping T, the nonsmooth convex function \(f\) and the step size \(\lambda _{k}\), we prove the convergence of the inexact hybrid projection-proximal point algorithm for solving generalized mixed variational inequalities in Hilbert spaces.

MSC:
49J40 Variational inequalities
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
47J25 Iterative procedures involving nonlinear operators
65K15 Numerical methods for variational inequalities and related problems
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