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Zbl 1225.49017
Noor, Muhammad Aslam
Projection iterative methods for solving some systems of general nonconvex variational inequalities. (English)
[J] Appl. Anal. 90, No. 5-6, 777-786 (2011). ISSN 0003-6811; ISSN 1563-504X/e

Summary: In this article, we introduce and consider a new system of general nonconvex variational inequalities involving four different operators. We use the projection operator technique to establish the equivalence between the system of general nonconvex variational inequalities and a fixed-point problem. This alternative equivalent formulation is used to suggest and analyse some new explicit iterative methods for this system of nonconvex variational inequalities. We also study the convergence analysis of the new iterative method under certain mild conditions. Since this new system includes the system of nonconvex variational inequalities, variational inequalities and related optimization problems as special cases, results obtained in this article continue to hold for these problems. Our results can be viewed as a refinement and an improvement of the previously known results for variational inequalities.

MSC 2000:: *49J40 Variational methods including variational inequalities
90C33 Complementarity problems
49M25 Finite difference methods

Keywords: general nonconvex variational inequalities; projection operator technique; fixed-point problem; explicit iterative methods

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