Augmented Lagrangian Techniques for Elliptic State Constrained Optimal Control Problems

Maïtine Bergounioux (1) , Karl Kunisch (2)

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

We propose augmented Lagrangian methods to solve state and control constrained optimal control problems. The approach is based on the Lagrangian formulation of nonsmooth convex optimization in Hilbert spaces . We investigate a linear optimal control problem with a boundary control function. Both the equation and the constraints are augmented. The proposed methods are general and can be adapted to a much wider class of problems.

Mots clés: State and Control Constrained Optimal Control Problems; Augmented Lagrangian; Elliptic Equations

Domaines: Optimisation et contrôle [math.OC]

Maïtine Bergounioux, Karl Kunisch. Augmented Lagrangian Techniques for Elliptic State Constrained Optimal Control Problems. SIAM Journal on Control and Optimization, 1997, 35, n°5, pp.1524-1543. ⟨hal-00023022⟩