Convergence of stationary sequences for variational inequalities with maximal monotone operators (Q687071)

The variational inequality \(0\in T(x)\) for a maximal monotone operator \(T\) defined on \({\mathbf R}^ n\) is considered. Given a stationary sequence \(\{x_ n\}\) for \(T\), i.e. \(T(x_ n)\to 0\), sufficient conditions are given which ensure that this sequence is also minimizing, assuming only that \(0\in\text{dom}(T^{-1})\). In the case when \(T\) is the subdifferential of a closed convex proper function, this improves and generalizes a similar result in convex analysis which was proved under the more stringent assumption \(0\in\text{ri dom}(T^{-1})\).