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Smoothing-Nonsmooth Reformulations of Variational Inequality Problems

It has long been known that variational inequality problems can be reformulated as nonsmooth equations. Recently, locally high-order convergent nonsmooth Newton methods for nonsmooth equations have been well established via the concept of semismoothness. In this paper, we focus our discussions on a way of globalizing nonsmooth Newton methods based on a smoothing-nonsmooth reformulation of nonsmooth equations. Various properties of the reformulated functions will be investigated and Newton-type methods will be applied to solve the reformulated systems.