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 appropr...

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Bibliographic Details
Published inMathematics and computers in simulation Vol. 79; no. 4; pp. 925 - 936
Main Author Gerdts, Matthias
Format Journal Article
LanguageEnglish
Published Elsevier B.V 15.12.2008
Subjects
Control-state constraints
Minimum principle
Nonsmooth Newton’s method
Optimal control
Minimum principle
Control-state constraints
Optimal control
Nonsmooth Newton’s method
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Summary: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.
ISSN:0378-4754
1872-7166
DOI:10.1016/j.matcom.2008.02.018