Primal worst and dual best in robust vector optimization

Lagrangian duality in set optimization with an application to robust multiobjective optimization. We establish a relationship between the robust counterpart of an uncertain cone-convex vector problem and the optimistic counterpart of its uncertain dual. Along the line marked by Beck and Ben-Tal (2009) in the scalar case, we show that operating in the primal problem with a pessimistic view is equivalent to operating with an optimistic approach in its dual.