Fernandez-Cara, Enrique , MARÍN GAYTE, IRENE
Si
Commun. Pure Appl. Anal
Article
Científica
1.916
1.077
01/04/2020
000507859700014
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.
Elliptic PDEs; Navier-Stokes equations; optimal control; bi-objective problems; Pareto equilibria; Dubovitskii-Milyutin formalism