Publication: Globalization of Pantoja's Optimal Control Algorithm
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Globalization of Pantoja's Optimal Control Algorithm

- incollection -
 

Author(s)
Bruce Christianson , Michael C. Bartholomew-Biggs

Published in
Automatic Differentiation of Algorithms: From Simulation to Optimization

Editor(s)
George Corliss, Christèle Faure, Andreas Griewank, Laurent Hascoët, Uwe Naumann

Year
2002

Publisher
Springer

Abstract
In 1983 Pantoja described a stagewise construction of the Newton direction for a general class of discrete time optimal control problems. His algorithm incurs amazingly low overheads: the cost (measured in target function evaluations) is independent of the number of discrete time-steps. The algorithm can be modified to verify that the Hessian contains no eigenvalues less than a postulated quantity, and to produce an appropriate descent direction in the case where the Hessian fails to be positive definite and global convergence becomes an issue. Coleman and Liao have proposed a specific damping strategy in this context. Here we describe how automatic differentiation can be used to implement Pantoja's algorithm, and we briefly consider some alternative globalization strategies, within which ad techniques can be further deployed.

Cross-References
Corliss2002ADo

BibTeX
@INCOLLECTION{
         Christianson2002GoP,
       author = "Bruce Christianson and Michael C. Bartholomew-Biggs",
       title = "Globalization of {P}antoja's Optimal Control Algorithm",
       pages = "125--130",
       chapter = "13",
       crossref = "Corliss2002ADo",
       booktitle = "Automatic Differentiation of Algorithms: From Simulation to Optimization",
       year = "2002",
       editor = "George Corliss and Christ{\`e}le Faure and Andreas Griewank and Laurent
         Hasco{\"e}t and Uwe Naumann",
       series = "Computer and Information Science",
       publisher = "Springer",
       address = "New York, NY",
       abstract = "In 1983 Pantoja described a stagewise construction of the Newton direction for a
         general class of discrete time optimal control problems. His algorithm incurs amazingly low
         overheads: the cost (measured in target function evaluations) is independent of the number of
         discrete time-steps. The algorithm can be modified to verify that the Hessian contains no
         eigenvalues less than a postulated quantity, and to produce an appropriate descent direction in the
         case where the Hessian fails to be positive definite and global convergence becomes an issue.
         Coleman and Liao have proposed a specific damping strategy in this context. Here we describe how
         automatic differentiation can be used to implement Pantoja's algorithm, and we briefly consider
         some alternative globalization strategies, within which AD techniques can be further deployed."
}


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