Imperial College London

ProfessorBenoitChachuat

Faculty of EngineeringDepartment of Chemical Engineering

Professor of Process Systems Engineering
 
 
 
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Contact

 

b.chachuat Website

 
 
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Location

 

609Roderic Hill BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Mitsos:2009:10.1137/080717341,
author = {Mitsos, A and Chachuat, B and Barton, PI},
doi = {10.1137/080717341},
journal = {SIAM Journal on Optimization},
pages = {573--601},
title = {McCormick-Based Relaxations of Algorithms},
url = {http://dx.doi.org/10.1137/080717341},
volume = {20},
year = {2009}
}

RIS format (EndNote, RefMan)

TY  - JOUR
AB - Theory and implementation for the global optimization of a wide class of algorithms is presented via convex/affine relaxations. The basis for the proposed relaxations is the systematic construction of subgradients for the convex relaxations of factorable functions by McCormick [Math. Prog., 10 (1976), pp. 147-175]. Similar to the convex relaxation, the subgradient propagation relies on the recursive application of a few rules, namely, the calculation of subgradients for addition, multiplication, and composition operations. Subgradients at interior points can be calculated for any factorable function for which a McCormick relaxation exists, provided that subgradients are known for the relaxations of the univariate intrinsic functions. For boundary points, additional assumptions are necessary. An automated implementation based on operator overloading is presented, and the calculation of bounds based on a. ne relaxation is demonstrated for illustrative examples. Two numerical examples for the global optimization of algorithms are presented. In both examples a parameter estimation problem with embedded differential equations is considered. The solution of the differential equations is approximated by algorithms with a fixed number of iterations.
AU - Mitsos,A
AU - Chachuat,B
AU - Barton,PI
DO - 10.1137/080717341
EP - 601
PY - 2009///
SN - 1052-6234
SP - 573
TI - McCormick-Based Relaxations of Algorithms
T2 - SIAM Journal on Optimization
UR - http://dx.doi.org/10.1137/080717341
VL - 20
ER -