Imperial College London

Prof Claire S. Adjiman FREng

Faculty of EngineeringDepartment of Chemical Engineering

Professor of Chemical Engineering



+44 (0)20 7594 6638c.adjiman Website




Ms Sevgi Thompson +44 (0)20 7594 1478




608Roderic Hill BuildingSouth Kensington Campus






BibTex format

author = {Nerantzis, D and Adjiman, C},
doi = {10.1007/s10898-018-0718-y},
journal = {Journal of Global Optimization},
pages = {467--483},
title = {Tighter αBB relaxations through a refi nement scheme for the scaled Gerschgorin theorem},
url = {},
volume = {73},
year = {2019}

RIS format (EndNote, RefMan)

AB - Of central importance to the αBB algorithm is the calculation of the α values that guarantee the convexity of the underestimator. Improvement (reduction) of these values can result in tighter underestimators and thus increase the performance of the algorithm. For instance, it was shown by Wechsung et al. (J Glob Optim 58(3):429-438, 2014) that the emergence of the cluster effect can depend on the magnitude of the α values. Motivated by this, we present a refinement method that can improve (reduce) the magnitude of α values given by the scaled Gerschgorin method and thus create tighter convex underestimators for the αBB algorithm. We apply the new method and compare it with the scaled Gerschgorin on randomly generated interval symmetric matrices as well as interval Hessians taken from test functions. As a measure of comparison, we use the maximal separation distance between the original function and the underestimator. Based on the results obtained, we conclude that the proposed refinement method can significantly reduce the maximal separation distance when compared to the scaled Gerschgorin method. This approach therefore has the potential to improve the performance of the αBB algorithm.
AU - Nerantzis,D
AU - Adjiman,C
DO - 10.1007/s10898-018-0718-y
EP - 483
PY - 2019///
SN - 0925-5001
SP - 467
TI - Tighter αBB relaxations through a refi nement scheme for the scaled Gerschgorin theorem
T2 - Journal of Global Optimization
UR -
UR -
VL - 73
ER -