An extragradient algorithm for solving general nonconvex variational inequalities. (English) Zbl 1193.49008

Summary: We suggest and analyze an extragradient method for solving general nonconvex variational inequalities using the technique of the projection operator. We prove that the convergence of the extragradient method requires only pseudomonotonicity, which is a weaker condition than requiring monotonicity. In this sense, our result can be viewed as an improvement and refinement of the previously known results. Our method of proof is very simple as compared with other techniques.


49J40 Variational inequalities
49M15 Newton-type methods
47J20 Variational and other types of inequalities involving nonlinear operators (general)
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