SIAM Journal on Control and Optimization / Optimal control for the elliptic system with polygonal state constraints

This work is devoted to stationary optimal control problems with polygonal constraints on the components of the state. Existence of Lagrange multipliers, of different regularities, is verified for the cases with and without Slater condition holding. For the numerical realization a semismooth Newton method is proposed for an appropriately chosen family of regularized problems. The asymptotic behavior of the regularized problem class is studied, and numerical feasibility of the method is shown.