RT journal article
T1 Pareto Optimality for Multioptimization of Continuous Linear Operators
A1 Cobos Sánchez, Clemente
A1 Vílchez Membrilla, José Antonio
A1 Campos Jiménez, Almudena
A1 García Pacheco, Francisco Javier
A2 Ingeniería en AutomáticaElectrónica, Arquitectura y Redes de Computadores
A2 Matemáticas
K1 multioptimization
K1 Pareto optimality
K1 linear operators
K1 adjoint operators
K1 normed spaces
K1 matrix norms
AB This manuscript determines the set of Pareto optimal solutions of certain multiobjective-optimization problems involving continuous linear operators defined on Banach spaces and Hilbert spaces. These multioptimization problems typically arise in engineering. In order to accomplish our goals, we first characterize, in an abstract setting, the set of Pareto optimal solutions of any multiobjective optimization problem. We then provide sufficient topological conditions to ensure the existence of Pareto optimal solutions. Next, we determine the Pareto optimal solutions of convex max-min problems involving continuous linear operators defined on Banach spaces. We prove that the set of Pareto optimal solutions of a convex max-min of form max parallel to T(x)parallel to, min parallel to x parallel to coincides with the set of multiples of supporting vectors of T. Lastly, we apply this result to convex max-min problems in the Hilbert space setting, which also applies to convex max-min problems that arise in the design of truly optimal coils in engineering.
PB MDPI
SN 2073-8994
YR 2021
FD 2021-04
LK http://hdl.handle.net/10498/24899
UL http://hdl.handle.net/10498/24899
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 09-nov-2026