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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Veröffentlicht in:Operations research letters Jg. 43; H. 4; S. 384 - 388
Hauptverfasser: Buchheim, Christoph, De Santis, Marianna, Palagi, Laura
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier B.V 01.07.2015
Schlagworte:
Global optimization
Integer programming
Quadratic programming
Integer programming
Quadratic programming
Global optimization
ISSN:0167-6377, 1872-7468
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Abstract 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.
AbstractList 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.
Author De Santis, Marianna
Palagi, Laura
Buchheim, Christoph
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  surname: Palagi
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  email: laura.palagi@uniroma1.it
  organization: Dipartimento di Ingegneria informatica automatica e gestionale A. Ruberti, Sapienza Università di Roma, Via Ariosto 25, 00185 Roma, Italy
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10.1007/s10878-012-9560-1
10.1007/s10898-011-9757-3
10.1080/10556789308805542
10.1007/BF01100205
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Issue 4
Keywords Integer programming
Quadratic programming
Global optimization
Language English
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Snippet We propose two exact approaches for non-convex quadratic integer minimization subject to linear constraints where lower bounds are computed by considering...
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SubjectTerms Global optimization
Integer programming
Quadratic programming
Title A fast branch-and-bound algorithm for non-convex quadratic integer optimization subject to linear constraints using ellipsoidal relaxations
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