Optimality Conditions for Minimization over the (Weakly or Properly) Efficient Set

The paper deals with the optimization problem of a nonlinear real function over the (weakly or properly) efficient set associated to a convex, multi-objective program in Banach spaces. Abstract optimality conditions are obtained via derivatives for set-valued functions. In the strict convex case these conditions lead to a nonlinear system Involving the (classical) derivatives up to the second order