In this paper, properties of differentiable gap functions for variational inequalities and convergence of the corresponding descent methods under a Hilbert space setting are considered. We give various convergence results under different assumptions on the cost mapping, including the monotone...

The problem of finding a solution to a system of variational inequalities, which can be interpreted as a generalization of a convex optimization problem under arbitrary right-hand side constraint perturbations, is considered. We suggest this problem to be converted into a mixed variational...