On the local uniqueness of solutions of variational inequalities under H-differentiability

Authors:
M. A. Tawhid
Affiliations:
Assistant Professor, Department of Mathematics, Faculty of Science, Alexandria University, Alexandria, Egypt
Venue:
Journal of Optimization Theory and Applications
Year:
2002

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Abstract

In this paper, we give some sufficient conditions for the local uniqueness of solutions to nonsmooth variational inequalities where the underlying functions are H-differentiable and the underlying set is a closed convex set/polyhedral set/box/polyhedral cone. We show how the solution of a linearized variational inequality is related to the solution of the variational inequality. These results extend/unify various similar results proved for C1 and locally Lipschitzian variational inequality problems. When specialized to the nonlinear complementarity problem, our results extend/unify those of C2 and C1 nonlinear complementarity problems.