Optimal control of the obstacle in semilinear variational inequalities

Maïtine Bergounioux (1) , Suzanne Sl Lenhart (2)

1 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans
2 Department of Mathematics [Tennessee]

We consider an optimal control problem where the state satisfies an obstacle type semilinear variational inequality and the control function is the obstacle. The state is chosen to be close to a desired profile while the obstacle is not too large in H1, and H2-bounded. We prove that an optimal control exists and give necessary optimality conditions, using approximation techniques.

Mots clés: Optimal control; obstacle problem; variational inequalities; semilinear elliptic equations

Domaines: Optimisation et contrôle [math.OC]

Maïtine Bergounioux, Suzanne Sl Lenhart. Optimal control of the obstacle in semilinear variational inequalities. Positivity, 2004, 8, pp. 229-242. ⟨hal-00022012⟩