A primal-dual active set algorithm for bilaterally control constrained optimal control problems

A generalized Moreau-Yosida based primal-dual active set algorithm for the solution of a representative class of bilaterally control constrained optimal control problems with boundary control is developed. The use of the generalized Moreau-Yosida approximation allows an efficient identification of the active and inactive sets at each iteration level. The method requires no step-size strategy and exhibits a finite termination property for the discretized problem class. In infinite as well as in finite dimensions a convergence analysis based on an augmented Lagrangian merit function is given. In a series of numerical tests the efficiency of the new algorithm is emphasized.