Optimal control of obstacle problems : existence of Lagrange multipliers

We study first order optimality systems for the control of a system governed by a variational inequality and deal with Lagrange multipliers : is it possible to associate to each pointwise constraint a multiplier to get a ``good'' optimality system ? We give positive and negative answers for the finite and infinite dimensional cases. These results are compared with the previous ones got by penalization or differentiation

Optimal Control of Obstacle Problems: Existence of Lagrange Multipliers

We study first order optimality systems for the control of a system governed by a variational inequality and deal with Lagrange multipliers: is it possible to associate to each pointwise constraint a multiplier to get a “good” optimality system? We give positive and negative answers for the finite and infinite dimensional cases. These results are compared with the previous ones got by penalization or differentiation