Proximal Methods for Variational Inequalities with Set-Valued Monotone Operators

A general approach to analyse convergence and rate of convergence of the proximal-like methods for variational inequalities with set-valued maximal monotone operators is developed. It is oriented to methods coupling successive approximation of the variational inequality with the proximal point algorithm as well as to related methods using regularization on a subspace and weak regularization. This approach seizes also so-called multi-step regularization methods, in which the number of proximal iterations in the approximated problems is controlled by a criterion characterizing these iterations as to be effective.