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Convergence rate of McCormick relaxations

Bompadre, Agustín and Mitsos, Alexander (2012) Convergence rate of McCormick relaxations. Journal of Global Optimization, 52 (1). pp. 1-28. ISSN 0925-5001. doi:10.1007/s10898-011-9685-2.

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Theory for the convergence order of the convex relaxations by McCormick (Math Program 10(1):147–175, 1976) for factorable functions is developed. Convergence rules are established for the addition, multiplication and composition operations. The convergence order is considered both in terms of pointwise convergence and of convergence in the Hausdorff metric. The convergence order of the composite function depends on the convergence order of the relaxations of the factors. No improvement in the order of convergence compared to that of the underlying bound calculation, e.g., via interval extensions, can be guaranteed unless the relaxations of the factors have pointwise convergence of high order. The McCormick relaxations are compared with the αBB relaxations by Floudas and coworkers (J Chem Phys, 1992, J Glob Optim, 1995, 1996), which guarantee quadratic convergence. Illustrative and numerical examples are given.

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Additional Information:© 2011 Springer Science+Business Media, LLC. Received: 8 July 2010. Accepted: 1 February 2011. Published online: 18 February 2011. We would like to thank Corey J. Noone for useful suggestions. We are grateful to Benoît Chachuat for providing libMC/MC++. We appreciate the thorough comments provided by the anonymous reviewers and editors which resulted in a significantly improved manuscript.
Subject Keywords:Nonconvex optimization; Global optimization; Convex relaxation; McCormick; AlphaBB; Interval extensions
Issue or Number:1
Record Number:CaltechAUTHORS:20120104-112212599
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Official Citation:Convergence rate of McCormick relaxations Agustín Bompadre and Alexander Mitsos
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:28646
Deposited By: Ruth Sustaita
Deposited On:04 Jan 2012 19:47
Last Modified:09 Nov 2021 16:59

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