Publication: Original Halley Method and its Improvement with Automatic Differentiation
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Original Halley Method and its Improvement with Automatic Differentiation

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Author(s)
Haibin Zhang , Lizhen Zhang , Sen Zhang

Published in
Sixth International Conference on Fuzzy Systems and Knowledge Discovery (FSKD 2009)

Year
2009

Publisher
IEEE

Abstract
Original Halley method, also referred to as the tangent hyperbolas method, is the classical third order method which can be used to solve the optimization problems. However, computing the derivative terms in solving the Halley equation becomes a key problem to reduce its computational cost. By using efficiently the techniques of automatic differentiation and preconditioned conjugate graduate method, original Halley method is established and improved in this paper. Theoretical and numerical results show that the improved version is more efficient than the original method.

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BibTeX
@INPROCEEDINGS{
         Zhang2009OHM,
       author = "Haibin Zhang and Lizhen Zhang and Sen Zhang",
       title = "Original {H}alley Method and its Improvement with Automatic Differentiation",
       booktitle = "Sixth International Conference on Fuzzy Systems and Knowledge Discovery (FSKD
         2009)",
       editor = "",
       pages = "351--355",
       publisher = "IEEE",
       abstract = "Original Halley method, also referred to as the tangent hyperbolas method, is the
         classical third order method which can be used to solve the optimization problems. However,
         computing the derivative terms in solving the Halley equation becomes a key problem to reduce its
         computational cost. By using efficiently the techniques of automatic differentiation and
         preconditioned conjugate graduate method, original Halley method is established and improved in this
         paper. Theoretical and numerical results show that the improved version is more efficient than the
         original method.",
       year = "2009",
       doi = "10.1109/FSKD.2009.125",
       volume = "4",
       keywords = "Halley method;automatic differentiation;optimization;preconditioned conjugate
         graduate method;tangent hyperbolas method;conjugate gradient methods;differentiation;optimisation;",
       ad_theotech = "Higher Order"
}


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