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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.
MSC:
49J40Variational methods including variational inequalities
49M15Newton-type methods in calculus of variations
47J20Inequalities involving nonlinear operators
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