  This paper addresses the study and characterizations of variational convexity
of extended-real-valued functions on Banach spaces. This notion has been
recently introduced by Rockafellar, and its importance has been already
realized and applied to continuous optimization problems in finite-dimensional
spaces. Variational convexity in infinite-dimensional spaces, which is studied
here for the first time, is significantly more involved and requires the usage
of powerful tools of geometric functional analysis together with variational
analysis and generalized differentiation in Banach spaces.
