Optimal control of a quasi-variational obstacle problem

Samir Adly (1) , Maïtine Bergounioux (2) , Mohamed Ait-Mansour (1)

1 DMI
2 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans

We consider an optimal control where the state-control relation is given by a quasi-variational inequality, namely a generalized obstacle problem. We give an existence result for solutions to such a problem. The main tool is a stability result, based on the Mosco-convergence theory, that gives the weak closeness of the control-to-state operator. We end the paper with some examples.

Mots clés: Mosco convergence; quasi-variational inequalities; Optimal control

Domaines: Optimisation et contrôle [math.OC]

Samir Adly, Maïtine Bergounioux, Mohamed Ait-Mansour. Optimal control of a quasi-variational obstacle problem. Journal of Global Optimization, 2010, 47 (3), pp.421-435. ⟨10.1007/s10898-008-9366-y⟩. ⟨hal-00092013v3⟩