Artículo
Bi-objective optimal control of some PDEs: Nash equilibria and quasi-equilibria
Autor/es | Fernández Cara, Enrique
Marín Gayte, Irene |
Departamento | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Fecha de publicación | 2021-05-05 |
Fecha de depósito | 2022-07-01 |
Publicado en |
|
Resumen | This paper deals with the solution of some multi-objective optimal control problems for
several PDEs: linear and semilinear elliptic equations and stationary Navier-Stokes systems. Speci -
cally, we look for Nash equilibria ... This paper deals with the solution of some multi-objective optimal control problems for several PDEs: linear and semilinear elliptic equations and stationary Navier-Stokes systems. Speci - cally, we look for Nash equilibria associated with standard cost functionals. For linear and semilinear elliptic equations, we prove the existence of equilibria and we deduce related optimality systems. For stationary Navier-Stokes equations, we prove the existence of Nash quasi-equilibria, i.e. solutions to the optimality system. In all cases, we present some iterative algorithms and, in some of them, we establish convergence results. For the existence and characterization of Nash quasi-equilibria in the Navier-Stokes case, we use the formalism of Dubovitskii and Milyutin. In this context, we also present a nite element approximation and we illustrate the techniques with numerical experiments. |
Cita | Fernández Cara, E. y Marín Gayte, I. (2021). Bi-objective optimal control of some PDEs: Nash equilibria and quasi-equilibria. ESAIM: Control, Optimisation and Calculus of Variations, 27, 50-1-50-30. |
Ficheros | Tamaño | Formato | Ver | Descripción |
---|---|---|---|---|
Bi-objective optimal control of ... | 2.308Mb | [PDF] | Ver/ | |