  In this paper, we present a new set-valued Lagrange multiplier theorem for
constrained convex set-valued optimization problems. We introduce the novel
concept of Lagrange process. This concept is a natural extension of the
classical concept of Lagrange multiplier where the conventional notion of
linear continuous operator is replaced by the concept of closed convex process,
its set-valued analogue. The behaviour of this new Lagrange multiplier based on
a process is shown to be particularly appropriate for some types of proper
minimal points and, in general, when it has a bounded base.
