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Formal global optimisation with Taylor models (2006)
| Venue: | Automated Reasoning, LNCS |
| Citations: | 12 - 0 self |
BibTeX
@INPROCEEDINGS{Zumkeller06formalglobal,
author = {Roland Zumkeller},
title = {Formal global optimisation with Taylor models},
booktitle = {Automated Reasoning, LNCS},
year = {2006},
pages = {408--422},
publisher = {Springer}
}
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Abstract
Abstract. Formal proofs and global optimisation are two research ar-eas that have been heavily influenced by the arrival of computers. This article aims to bring both further together by formalising a global optimi-sation method based on Taylor models: a set of functions is represented by a polynomial together with an error bound. The algorithms are imple-mented 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. 1
Keyphrases
taylor model formal global optimisation polynomial bounding technique polynomial together efficient way proof assistant coq research ar-eas constructive real number formal proof global optimi-sation method ultimate goal term language multi-variate smooth function global optimisation proven bound error bound
