Optimal control of an elastic–rigid obstacle problem

Abstract

In this paper, we consider the optimal control problem of an elastic–rigid obstacle problem. The force is considered as the control, and the corresponding solution to the elastic–rigid obstacle problem is taken to be the state. An approximate optimization problem is proposed by regularizing the original non-differentiable constrained problem, and the connection between the two formulations is established through some convergence results. Existence of optimal pairs is proved and necessary optimality conditions are derived.