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Iterative methods for general nonconvex variational inequalities. (English) Zbl 1213.49017

Summary: We introduce and consider some new classes of variational inequalities and the Wiener-Hopf equations. Using the projection technique, we establish the equivalence between the general nonconvex variational inequalities and fixed point problems as well as Wiener-Hopf equations. This alternative equivalent formulation is used to study the existence of a solution of general convex variational inequalities. This equivalence is used to suggest and analyze several projection iterative methods for solving the general nonconvex variational inequalities. Convergence criteria of these new iterative methods are also discussed under suitable conditions. Our method of proofs is very simple as compared with other techniques.

MSC:

49J40 Variational inequalities
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
47H10 Fixed-point theorems
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