Locally unique solutions of nonsmooth general variational inequalities

Abstract

We study nonsmooth general variational inequalities where the underlying functions admit the H -differentiability but are not necessarily locally Lipschitzian nor directionally differentiable, and the underlying set is a closed convex set/polyhedral set/box/polyhedral cone. We give some sufficient conditions to guarantee the local uniqueness of solutions to nonsmooth general variational inequalities. Also, we show how the solution of a linearized general variational inequality is related to the solution of the general variational inequality. When specialized to the classical variational inequality and nonlinear complementarity problems, our results extend/unify various similar results proved for C 1 and locally Lipschitzian.