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 = {Kazazakis, N and Adjiman, CSJ},
doi = {10.1007/s10898-018-0632-3},
journal = {Journal of Global Optimization},
pages = {815--844},
title = {Arbitrarily tight aBB underestimators of general non-linear functions over sub-optimal domains},
url = {},
volume = {71},
year = {2018}

RIS format (EndNote, RefMan)

AB - In this paper we explore the construction of arbitrarily tight αBB relaxations of C2 general non-linear non-convex functions. We illustrate the theoretical challenges of building such relaxations by deriving conditions under which it is possible for an αBB underestimator to provide exact bounds. We subsequently propose a methodology to build αBB underestimators which may be arbitrarily tight (i.e., the maximum separation distance between the original function and its underestimator is arbitrarily close to 0) in some domains that do not include the global solution (defined in the text as “sub-optimal”), assuming exact eigenvalue calculations are possible. This is achieved using a transformation of the original function into a μ-subenergy function and the derivation of αBB underestimators for the new function. We prove that this transformation results in a number of desirable bounding properties in certain domains. These theoretical results are validated in computational test cases where approximations of the tightest possible μ-subenergy underestimators, derived using sampling, are compared to similarly derived approximations of the tightest possible classical αBB underestimators. Our tests show that μ-subenergy underestimators produce much tighter bounds, and succeed in fathoming nodes which are impossible to fathom using classical αBB.
AU - Kazazakis,N
AU - Adjiman,CSJ
DO - 10.1007/s10898-018-0632-3
EP - 844
PY - 2018///
SN - 0925-5001
SP - 815
TI - Arbitrarily tight aBB underestimators of general non-linear functions over sub-optimal domains
T2 - Journal of Global Optimization
UR -
UR -
VL - 71
ER -