Convergence analysis of Taylor models and McCormick-Taylor models

Agustín Bompadre (), Alexander Mitsos () and Benoît Chachuat ()

Journal of Global Optimization, 2013, vol. 57, issue 1, 75-114

Abstract: This article presents an analysis of the convergence order of Taylor models and McCormick-Taylor models, namely Taylor models with McCormick relaxations as the remainder bounder, for factorable functions. Building upon the analysis of McCormick relaxations by Bompadre and Mitsos (J Glob Optim 52(1):1–28, 2012 ), convergence bounds are established for the addition, multiplication and composition operations. It is proved that the convergence orders of both qth-order Taylor models and qth-order McCormick-Taylor models are at least q + 1, under relatively mild assumptions. Moreover, it is verified through simple numerical examples that these bounds are sharp. A consequence of this analysis is that, unlike McCormick relaxations over natural interval extensions, McCormick-Taylor models do not result in increased order of convergence over Taylor models in general. As demonstrated by the numerical case studies however, McCormick-Taylor models can provide tighter bounds or even result in a higher convergence rate. Copyright Springer Science+Business Media New York 2013

Keywords: Nonconvex optimization; Global optimization; Convex relaxations; McCormick relaxations; Taylor models; McCormick-Taylor models; Interval extensions; Convergence rate (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (9)

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DOI: 10.1007/s10898-012-9998-9

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