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

Authors:
Matthias Gerdts
Affiliations:
School of Mathematics, University of Birmingham, Edgbaston, Birmingham B15 2TT, United Kingdom
Venue:
Mathematics and Computers in Simulation
Year:
2008

Citing 4
Cited 3

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Abstract

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.