April  2008, 4(2): 247-270. doi: 10.3934/jimo.2008.4.247

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, United Kingdom

2. 

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

Received  March 2007 Revised  September 2007 Published  April 2008

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.
Citation: Matthias Gerdts, Martin Kunkel. A nonsmooth Newton's method for discretized optimal control problems with state and control constraints. Journal of Industrial & Management Optimization, 2008, 4 (2) : 247-270. doi: 10.3934/jimo.2008.4.247
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