Optimality Conditions and Generalized Bang-Bang Principle for a State Constrained Semilinear Parabolic Problem

Maïtine Bergounioux (1) , Fredi Tröltzsch (2)

1 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans
2 Faculty of Mathematics

We consider a distributed optimal control problem governed by a semilinear parabolic equation, where constraints on the control and on the state are given. Aiming to show the existence of regular Lagrange multipliers we follow a linearization approach together with a two-norm technique. The theory is applied to derive a generalized bang-bang principle.

Mots clés: Semilinear equations; Qualification condition; Optimal control

Domaines: Optimisation et contrôle [math.OC]

Maïtine Bergounioux, Fredi Tröltzsch. Optimality Conditions and Generalized Bang-Bang Principle for a State Constrained Semilinear Parabolic Problem. Numerical Functional Analysis and Applications, 1996, 15, n° 5 & 6, pp.517-537. ⟨hal-00023061⟩