Stable solution of variational inequalities with composed monotone operators

Convergence of proximal-based methods is analysed for variational inequalities with operators of the type T-0 + partial derivative F, where T-0 is a single-valued, hemicontinuous and monotone operator and partial derivative F is the subdifferential of a proper convex lower semicontinuous functional. The analysis 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. Conditions ensuring linear convergence are established. Finally, we observe briefly some classes of problems which can be solved by means of the methods considered.