Some classes of general nonconvex variational inequalities. (English) Zbl 1213.49018

Summary: We introduce and consider a new class of variational inequalities, which is called the general nonconvex variational inequality. We establish the equivalence between general nonconvex variational inequalities and fixed point problems as well as the Wiener-Hopf equations using the projection method. This alternative equivalent formulation is used to study the existence of a solution of general convex variational inequalities. We also use this equivalence formulation to suggest some iterative methods. 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.


49J40 Variational inequalities
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
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