Active Set Strategy for Constrained Optimal Control Problems : the Finite Dimensional Case

Maïtine Bergounioux (1) , Karl Kunisch (2)

1 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans
2 IM - Institut für Mathematik [Graz]

We consider control constrained and state constrained optimal control problems governed by elliptic partial differential equations, once they have been discretized. We propose and analyze an algorithm for efficient solution of these finite dimensional problems. It is based on an active set strategy involving primal as well as dual variables and is suggested by a generalized Moreau-Yosida regularization of the control (or state) constraint. Sufficient conditions for convergence in finitely many iterations are given. At last we present numerical examples and discuss the role of the strict complementarity condition.

Mots clés: Moreau-Yosida approximation; augmented Lagrangian; primal-dual method; optimal control; active sets

Domaines: Optimisation et contrôle [math.OC]

Maïtine Bergounioux, Karl Kunisch (Dir.). Active Set Strategy for Constrained Optimal Control Problems : the Finite Dimensional Case. V.H. Nguyen, J.J. Strodiot and P. Tossings. Springer-Verlag, 1999. ⟨hal-00023014⟩