Publication: Taylor Series Models in Deterministic Global Optimization
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Taylor Series Models in Deterministic Global Optimization

- incollection -
 

Author(s)
R. Baker Kearfott , Alvard Arazyan

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
Deterministic global optimization requires a global search with rejection of subregions. To reject a subregion, bounds on the range of the constraints and objective function can be used. Although often effective, simple interval arithmetic sometimes gives impractically large bounds on the ranges. However, Taylor models as developed by Berz et al. may be effective in this context. Efficient incorporation of such models in a general global optimization package is a significant project. Here, we use the system COSY INFINITY by Berz et al. to study the bounds on the range of various order Taylor models for certain difficult test problems we have previously encountered. Based on that, we conclude that Taylor models may be useful for some, but not all, problems in verified global optimization. Forthcoming improvements in the COSY INFINITY interface will help us reach stronger conclusions.

Cross-References
Corliss2002ADo

BibTeX
@INCOLLECTION{
         Kearfott2002TSM,
       author = "R. Baker Kearfott and Alvard Arazyan",
       editor = "George Corliss and Christ{\`e}le Faure and Andreas Griewank and Laurent
         Hasco{\"e}t and Uwe Naumann",
       title = "Taylor Series Models in Deterministic Global Optimization",
       booktitle = "Automatic Differentiation of Algorithms: From Simulation to Optimization",
       series = "Computer and Information Science",
       pages = "365--372",
       publisher = "Springer",
       address = "New York, NY",
       crossref = "Corliss2002ADo",
       abstract = "Deterministic global optimization requires a global search with rejection of
         subregions. To reject a subregion, bounds on the range of the constraints and objective function can
         be used. Although often effective, simple interval arithmetic sometimes gives impractically large
         bounds on the ranges. However, Taylor models as developed by Berz et al. may be effective in this
         context. Efficient incorporation of such models in a general global optimization package is a
         significant project. Here, we use the system COSY Infinity by Berz et al. to study the bounds on the
         range of various order Taylor models for certain difficult test problems we have previously
         encountered. Based on that, we conclude that Taylor models may be useful for some, but not all,
         problems in verified global optimization. Forthcoming improvements in the COSY Infinity interface
         will help us reach stronger conclusions.",
       referred = "[Makino2002NAo]",
       year = "2002",
       chapter = "44"
}


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