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BibTex format

author = {Bompadre, A and Mitsos, A and Chachuat, B},
doi = {10.1007/s10898-012-9998-9},
journal = {Journal of Global Optimization},
pages = {75--114},
title = {Convergence analysis of Taylor models and McCormick-Taylor models},
url = {},
volume = {57},
year = {2012}

RIS format (EndNote, RefMan)

AB - 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.
AU - Bompadre,A
AU - Mitsos,A
AU - Chachuat,B
DO - 10.1007/s10898-012-9998-9
EP - 114
PY - 2012///
SN - 1573-2916
SP - 75
TI - Convergence analysis of Taylor models and McCormick-Taylor models
T2 - Journal of Global Optimization
UR -
UR -
UR -
VL - 57
ER -