The Lagrangian Process and Sensitivity in Constrained Convex Set-Valued Optimization Problems

M. A. Melguizo Padial, F. García Castaño

In this talk I present a new set-valued Lagrange multiplier rule for constrained convex set-valued optimization problems. I introduce the concept of Lagrange process, a set-valued extension of the classical concept of Lagrange multiplier where the conventional notion of linear continuous operator is replaced by its set-valued analogue, the concept of closed convex process. I also report some connections of this new set-valued multiplier with the sensitivity of the program.

Keywords: Lagrange multiplier; convex vector optimization; process; optimality condition

J. E. Martínez Legaz, V. Roshchina, M. Todorov

B. Jiménez, V. Novo, A. Vílchez Medina

J. Parra López, M. J. Cánovas Cánovas, M. A. López Cerdá, B. Mordukhovich