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Projection-proximal methods for general variational inequalities. (English) Zbl 1086.49005
Summary: We consider and analyze some new projection-proximal methods for solving general variational inequalities. The modified methods converge for pseudomonotone operators which is a weaker condition than monotonicity. The proposed methods include several new and known methods as special cases. Our results can be considered as a novel and important extension of the previously known results. Since the general variational inequalities include the quasi-variational inequalities and implicit complementarity problems as special cases, results proved in this paper continue to hold for these problems.
MSC:
49J40Variational methods including variational inequalities
90C33Complementarity and equilibrium problems; variational inequalities (finite dimensions)
47J20Inequalities involving nonlinear operators