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.

• Type: Journal
• Year: 2008
• Where: MCS
• Authors: Matthias Gerdts
• Keywords: Local Minimum Principle, MCS 2008, Minimum Principle, Nonsmooth Equation, Pattern Recognition