A geometrical approach to the Lagrange process through a new type of Lagrange duality in set-valued convex programming
In this talk we focus on the concept of Lagrangian process associated to a set-valued convex program. We state some conditions under which it becomes an optimal dual solution for a new Lagrangian-type duality scheme based on the use of processes as dual variables. Under these conditions, we also show that the Lagrangian process becomes a useful tool for measuring the sensitivity of the primal program. This new duality scheme is based on a new set-valued Lagrangian multiplier theorem from which we derive a strong duality result that guarantees the existence of optimal dual solutions even if the optimal point in the primal program is not reached in a feasible solution. The approach is essentially geometric.
Palabras clave: Lagrangian process set-valued duality