- Tytuł:
- A Nash equilibrium approach for multiobjective optimal control problems with elliptic partial differential equations
- Autorzy:
- Dreves, A.
- Powiązania:
- https://bibliotekanauki.pl/articles/206122.pdf
- Data publikacji:
- 2016
- Wydawca:
- Polska Akademia Nauk. Instytut Badań Systemowych PAN
- Tematy:
-
multiobjective optimization
generalized Nash equilibrium
optimal control problem
elliptic partial differential equation
finite elements
interior point method - Opis:
- We consider the generalized Nash equilibrium as a solution concept for multiobjective optimal control problems governed by elliptic partial differential equations with constraints not only for the control but also for the state variables. In the first part, we present a constructive proof of the existence of a generalized Nash equilibrium via an approximating sequence of suitable finite dimensional discretizations. In the second part, we propose a variant of a potential reduction algorithm for the numerical solution of these discretized problems. In contrast to the existing numerical approaches ours does not require the computation of the control–to–state mapping. Instead we introduce different state variables and guarantee that they become equal at a solution. We prove sufficient conditions for the convergence of our algorithm to a solution. Furthermore, some numerical results showing the applicability are provided.
- Źródło:
-
Control and Cybernetics; 2016, 45, 4; 457-482
0324-8569 - Pojawia się w:
- Control and Cybernetics
- Dostawca treści:
- Biblioteka Nauki
Artykuł