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2008, Volume 4, Issue 2: 247-270. Doi: 10.3934/jimo.2008.4.247
This issue Previous Article Finite difference approximation for stochastic optimal stopping problems with delays Next Article New approach to global minimization of normal multivariate polynomial based on tensor

A nonsmooth Newton's method for discretized optimal control problems with state and control constraints

  • 1.

    School of Mathematics, University of Birmingham, Edgbaston, Birmingham B15 2TT

  • 2.

    Department of Mathematics, University of Hamburg, Bundesstrasse 55, 20146 Hamburg

Received:  February 28, 2007
Revised:  August 31, 2007
Published:  March 2008
Abstract Related Papers Cited by
    Abstract
  • We investigate a nonsmooth Newton's method for the numerical solution of discretized optimal control problems subject to pure state constraints and mixed control-state constraints. The infinite dimensional problem is discretized by application of a general one-step method to the differential equation. By use of the Fischer-Burmeister function the first order necessary conditions for the discretized problem are transformed into an equivalent nonlinear and nonsmooth equation. This nonlinear and nonsmooth equation is solved by a globally convergent nonsmooth Newton's method. Numerical examples for the minimum energy problem and the optimal control of a robot conclude the article.
    Mathematics Subject Classification: Primary: 49J15, 49J52; Secondary: 49M15.

    Citation:
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