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Zbl 1171.58307
Noor, Muhammad Aslam
Projection methods for nonconvex variational inequalities. (English)
[J] Optim. Lett. 3, No. 3, 411-418 (2009). ISSN 1862-4472; ISSN 1862-4480/e

Summary: We introduce and consider a new class of variational inequalities, which is called the nonconvex variational inequalities. We establish the equivalence between the nonconvex variational inequalities and the fixed-point problems using the projection technique. This equivalent formulation is used to discuss the existence of a solution of the nonconvex variational inequalities. We also use this equivalent alternative formulation to suggest and analyze a new iterative method for solving the nonconvex variational inequalities. We also discuss the convergence of the iterative method under suitable conditions. Our method of proof is very simple as compared with other techniques.

MSC 2000:: *58E35 Variational inequalities (global problems)

Keywords: monotone operators; iterative method; resolvent operator; convergence

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Zentralblatt MATH Berlin [Germany]