Formal Global Optimisation with Taylor Models

  • Roland Zumkeller
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4130)


Formal proofs and global optimisation are two research areas that have been heavily influenced by the arrival of computers. This article aims to bring both further together by formalising a global optimisation method based on Taylor models: a set of functions is represented by a polynomial together with an error bound. The algorithms are implemented in the proof assistant Coq’s term language, with the ultimate goal to obtain formally proven bounds for any multi-variate smooth function in an efficient way. To this end we make use of constructive real numbers, interval arithmetic, and polynomial bounding techniques.


Formal Proof Interval Arithmetic Interval Bound Global Optimisation Method Addition Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Roland Zumkeller
    • 1
  1. 1.École PolytechniquePalaiseau CedexFrance

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