Convergence of diagonally stationary sequences in convex optimization (Q1332534)

In convex optimization, many approximation methods generate a ``diagonally stationary sequence'', or more precisely, a sequence \(\{x_ n\}\) in \(X\), for which exists \(x^*_ n \in \partial f^ n(x_ n)\) such that \(\| x^*_ n \|_ * \to 0\) for \(n \to \infty\), where \(X\) is a real normed linear space, \(f\) and \(f^ n\) be extended real- valued proper closed convex functions on \(X\). The paper explores convergence conditions of such sequences, and gives some general convergence results by applying variational convergence theory.