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.


49J40 Variational inequalities
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
47J20 Variational and other types of inequalities involving nonlinear operators (general)
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