A nonsmooth Newton’s method for control-state constrained optimal control problems

We investigate optimal control problems subject to mixed control-state constraints. The necessary conditions are stated in terms of a local minimum principle. By use of the Fischer-Burmeister function the minimum principle is transformed into an equivalent nonlinear and nonsmooth equation in appropriate Banach spaces. This nonlinear and nonsmooth equation is solved by a nonsmooth Newton's method. We will show the local quadratic convergence under certain regularity conditions and Suggest a globalization strategy based on the minimization of the squared residual norm. A numerical example for the Rayleigh problem concludes the article. (C) 2008 IMACS. Published by Elsevier B.V. All rights reserved.