A remark on the relation between the Tykhonov regularization and constraint relaxation for an optimal control problem Original Research Article

The aim of this paper is to prove that the approximate solutions of a linear optimal control problem obtained by a Tykhonov regularization are equal to the solutions obtained by relaxing the constraint of the control problem. The second method formulates an approximate optimal control problem and uses the Fenchel duality. Moreover, an algorithm to compute the optimal control formulated with the Fenchel duality is given, and its convergence is proved.