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Zbl 1193.49008
Noor, Muhammad Aslam
An extragradient algorithm for solving general nonconvex variational inequalities. (English)
[J] Appl. Math. Lett. 23, No. 8, 917-921 (2010). ISSN 0893-9659

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 2000:: *49J40 Variational methods including variational inequalities
49M15 Methods of Newton-Raphson, Galerkin and Ritz types
47J20 Inequalities involving nonlinear operators

Keywords: variational inequalities; nonconvex sets; monotone operators; iterative method; convergence

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Zentralblatt MATH Berlin [Germany]