Gayte-Delgado, I. , MARÍN GAYTE, IRENE
No
Optimization
Article
Científica
01/08/2024
001281595100001
2-s2.0-85200032173
This paper deals with the solution of some multi-objective optimal control problems for stationary Navier-Stokes equations. More precisely, we look for Pareto and Nash equilibria associated to standard cost functionals. First, we prove the existence of equilibria and we deduce appropriate optimality systems. Then, we analyse the existence and characterization of Pareto and Nash equilibria for the Navier-Stokes equations. Here, we use the formalism of Dubovitskii and Milyoutin., see [Girsanov FV. Lectures on mathematical theory of extremum problems. Berlin: Springer-Verlag; 1972. (Notes in economics and mathematical systems; vol. 67)]. Finally, we also present a finite element approximation of the bi-objective problem, we illustrate the techniques with several numerical experiments and we compare the Pareto and Nash equilibria.
Elliptic PDEs; Navier-Stokes equations; optimal control; Bi-objective problems; Pareto and Nash equilibria; Dubovitskii-Milyutin formalism