Imperial College London
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ProfessorAbbasEdalat

Faculty of Engineering, Department of Computing

Professor in Computer Science & Maths
 
 
 
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Contact

 

+44 (0)20 7594 8245a.edalat Website

 
 
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Location

 

420Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@inproceedings{Edalat:2018:10.1007/978-3-319-89366-2_25,
author = {Edalat, A and Maleki, M},
doi = {10.1007/978-3-319-89366-2_25},
pages = {459--475},
publisher = {Springer International Publishing},
title = {Differential calculus with imprecise input and its logical framework},
url = {http://dx.doi.org/10.1007/978-3-319-89366-2_25},
year = {2018}
}
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RIS format (EndNote, RefMan)

TY  - CPAPER
AB  - We develop a domain-theoretic Differential Calculus for locally Lipschitz functions on finite dimensional real spaces with imprecise input/output. The inputs to these functions are hyper-rectangles and the outputs are compact real intervals. This extends the domain of application of Interval Analysis and exact arithmetic to the derivative. A new notion of a tie for these functions is introduced, which in one dimension represents a modification of the notion previously used in the one-dimensional framework. A Scott continuous sub-differential for these functions is then constructed, which satisfies a weaker form of calculus compared to that of the Clarke sub-gradient. We then adopt a Program Logic viewpoint using the equivalence of the category of stably locally compact spaces with that of semi-strong proximity lattices. We show that given a localic approximable mapping representing a locally Lipschitz map with imprecise input/output, a localic approximable mapping for its sub-differential can be constructed, which provides a logical formulation of the sub-differential operator.
AU  - Edalat,A
AU  - Maleki,M
DO  - 10.1007/978-3-319-89366-2_25
EP  - 475
PB  - Springer International Publishing
PY  - 2018///
SP  - 459
TI  - Differential calculus with imprecise input and its logical framework
UR  - http://dx.doi.org/10.1007/978-3-319-89366-2_25
UR  - http://hdl.handle.net/10044/1/57660
ER  -
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