A geometrical approach to the Lagrange process through a new type of Lagrange duality in set-valued convex programming

M. A. Melguizo-Padial, F. García Castaño

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.

Keywords: Lagrangian, process, set-valued, duality

GT13.OPTCONT2 Invited Session
November 8, 2023  4:00 PM
HC1: Canónigos Room 1

F. García Castaño, M. A. Melguizo-Padial, G. Parzanese

M. Á. Sama Meige, A. Khan

G. Ruiz-Garzón, R. Osuna-Gómez, A. Rufián-Lizana, A. Beato-Moreno