Optimal control of a system governed by an elliptic partial differential equation

In this paper, we consider the existence and uniqueness of a state constrained boundary control problem governed by an elliptic partial differential equation with twice differentiable conditions on the state constraint. A linear reformulation of the minimax control problem has advantages which are enhanced by considering the implications of the continuous and discrete maximum principles. The continuous optimality conditions of the linear reformulation of the control problem are developed and stated in an algebraic setting.