Optimality conditions for proper solutions in multiobjective optimization with a polyhedral cone

L. Huerga, C. Gutiérrez Vaquero, B. Jiménez, V. Novo

In the framework of a multiobjective optimization problem with a polyhedral ordering cone, we characterize proper efficient solutions through linear and nonlinear scalarization, and we derive necessary and sufficient optimality conditions for this type of solutions.
For this aim, we use a kind of polyhedral dilating cones whose construction facilitates their handling and lets us provide scalarization results with a better tractability, since they are defined by a perturbation of the matrix that determines the ordering cone.

Keywords: Multiobjective optimization proper efficiency optimality conditions polyhedral ordering cone

J. Ruckmann, D. Hernandez

C. Gutiérrez Vaquero

G. Ruiz Garzón, R. Osuna Gómez, A. Rufián Lizana, B. Hernández Jiménez, J. Ruiz Zapatero