On a Lagrange-Newton method for a nonlinear parabolic boundary control problem

An optimal control problem governed by the heat equation with nonlinear boundary conditions is considered. The objective functional consists of a quadratic terminal part and a quadratic regularization term. On transforming the associated optimality system to a generalized equation. an SQP method for solving the optimal control problem is related to the Newton method for the generalized equation. In this way, the convergence of the SQP method is shown by proving the strong regularity of the optimality system. After explaining the numerical implementation of the theoretical results some high precision test examples are presented.