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

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  • Gerdts, Matthias

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.

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  • Gerdts, Matthias, 2008. "A nonsmooth Newton’s method for control-state constrained optimal control problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(4), pages 925-936.
    • Handle: RePEc:eee:matcom:v:79:y:2008:i:4:p:925-936
    DOI: 10.1016/j.matcom.2008.02.018
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    References listed on IDEAS

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    1. M. Gerdts, 2003. "Direct Shooting Method for the Numerical Solution of Higher-Index DAE Optimal Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 117(2), pages 267-294, May.
    2. Liqun Qi, 1993. "Convergence Analysis of Some Algorithms for Solving Nonsmooth Equations," Mathematics of Operations Research, INFORMS, vol. 18(1), pages 227-244, February.
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    Cited by:

    1. Bin Li & Chang Jun Yu & Kok Lay Teo & Guang Ren Duan, 2011. "An Exact Penalty Function Method for Continuous Inequality Constrained Optimal Control Problem," Journal of Optimization Theory and Applications, Springer, vol. 151(2), pages 260-291, November.

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