Chebyshev model arithmetic for factorable functions

Jai Rajyaguru, Mario E. Villanueva, Boris Houska and Benoît Chachuat ()
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Jai Rajyaguru: Imperial College London
Mario E. Villanueva: Imperial College London
Boris Houska: ShanghaiTech University
Benoît Chachuat: Imperial College London

Journal of Global Optimization, 2017, vol. 68, issue 2, No 9, 413-438

Abstract: Abstract This article presents an arithmetic for the computation of Chebyshev models for factorable functions and an analysis of their convergence properties. Similar to Taylor models, Chebyshev models consist of a pair of a multivariate polynomial approximating the factorable function and an interval remainder term bounding the actual gap with this polynomial approximant. Propagation rules and local convergence bounds are established for the addition, multiplication and composition operations with Chebyshev models. The global convergence of this arithmetic as the polynomial expansion order increases is also discussed. A generic implementation of Chebyshev model arithmetic is available in the library MC++. It is shown through several numerical case studies that Chebyshev models provide tighter bounds than their Taylor model counterparts, but this comes at the price of extra computational burden.

Keywords: Global optimization; Factorable functions; Chebyshev models; Taylor models; Interval analysis; Convergence rate (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10898-016-0474-9

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