V-subdifferentials of convex operators (Q1076957)

Let \(f: C\to F\) be a convex operator defined on a convex set C of a topological vector space E, let F be another topological vector space endowed with a convex cone \(F_+\). A notion of V-subdifferential \(\partial_ V f(a)\) of f at \(a\in C\) is introduced. Various properties of V-subdifferentials are studied and applications to differentiability of f are discussed. If \(F=R\), the V-subdifferential is equivalent to the notion of \(\epsilon\)-subdifferential. Nevertheless, the V-subdifferential has many properties which are not satisfied by the \(\epsilon\)- subdifferential whenever int \(F_+=\emptyset\).