Optimal control of the obstacle in a quasilinear elliptic variational inequality

this paper we consider an obstacle control problem where the state satisfies a quasilinear elliptic variational inequality and the control function is the obstacle. The state is chosen to be close to the desire profile while the H2 norms of the obstacle is not too large. Existence and necessary conditions for the optimal control are established.  2004 Elsevier Inc. All rights reserved