A fast branch-and-bound algorithm for non-convex quadratic integer optimization subject to linear constraints using ellipsoidal relaxations

We propose two exact approaches for non-convex quadratic integer minimization subject to linear constraints where lower bounds are computed by considering ellipsoidal relaxations of the feasible set. In the first approach, we intersect the ellipsoids with the feasible linear subspace. In the second...

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Bibliographic Details
Published inOperations research letters Vol. 43; no. 4; pp. 384 - 388
Main Authors Buchheim, Christoph, De Santis, Marianna, Palagi, Laura
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.07.2015
Subjects
Global optimization
Integer programming
Quadratic programming
Integer programming
Quadratic programming
Global optimization
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Summary:We propose two exact approaches for non-convex quadratic integer minimization subject to linear constraints where lower bounds are computed by considering ellipsoidal relaxations of the feasible set. In the first approach, we intersect the ellipsoids with the feasible linear subspace. In the second approach we penalize exactly the linear constraints. We investigate the connection between both approaches theoretically. Experimental results show that the penalty approach significantly outperforms CPLEX on problems with small or medium size variable domains.
ISSN:0167-6377
1872-7468
DOI:10.1016/j.orl.2015.05.001