Interior Proximal Method for Variational Inequalities: Case of Nonparamonotone Operators

For variational inequalities characterizing saddle points of Lagrangians associated with convex programming problems in Hilbert spaces, the convergence of an interior proximal method based on Bregman distance functionals is studied. The convergence results admit a successive approximation of the variational inequality and an inexact treatment of the proximal iterations.An analogous analysis is performed for finite-dimensional complementarity problems with multi-valued monotone operators.