On conjugate maps and directional derivatives of convex vector functions (Q5954627)

Given a set-valued map \(F: \mathbb{R}^n\rightrightarrows \mathbb{R}^m\) and an order relation on \(\mathbb{R}^m\) defined by a closed, convex, pointed cone, the paper introduces a concept of conjugate of \(F\) and studies its properties. Also, some properties relating the directional derivative of vector-valued convex functions \(f:\mathbb{R}^n\to \mathbb{R}^m\) and their subdifferentials are given.