| Título |
THEORETICAL AND NUMERICAL RESULTS FOR SOME BI-OBJECTIVE OPTIMAL CONTROL PROBLEMS |
| Autores |
Fernandez-Cara, Enrique , MARÍN GAYTE, IRENE |
| Publicación externa |
Si |
| Medio |
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS |
| Alcance |
Article |
| Naturaleza |
Científica |
| Cuartil JCR |
1 |
| Cuartil SJR |
1 |
| Impacto JCR |
1.916 |
| Impacto SJR |
1.077 |
| Fecha de publicacion |
01/04/2020 |
| ISI |
000507859700014 |
| DOI |
10.3934/cpaa.2020093 |
| Abstract |
This article deals with the solution of some multi-objective optimal control problems for several PDEs: linear and semilinear elliptic equations and stationary Navier-Stokes systems. More precisely, we look for Pareto equilibria associated to standard cost functionals. First, we study the linear and semilinear cases. We prove the existence of equilibria, we deduce appropriate optimality systems, we present some iterative algorithms and we establish convergence results. Then, we analyze the existence and characterization of Pareto equilibria for the Navier-Stokes equations. Here, we use the formalism of Dubovitskii and Milyutin. In this framework, we also present a finite element approximation of the bi-objective problem and we illustrate the techniques with several numerical experiments. |
| Palabras clave |
Elliptic PDEs; Navier-Stokes equations; optimal control; bi-objective problems; Pareto equilibria; Dubovitskii-Milyutin formalism |
| Miembros de la Universidad Loyola |
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