Formal Global Optimisation with Taylor Models

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

Abstract

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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

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

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