Mixed complementarity problems: regularity, estimates for the distance to a solution, and Newton methods

A variational inequality on a parallelepiped is considered. Many mathematical problems can be reduced to this type of model, for example nonlinear systems of equations, complementarity problems, and systems of Karush-Kuhn-Tucker-type. Estimates for the distance to a solution are given. For finding the set of active indices a Newton-type method with globalization is constructed.