We propose a branch-and-bound algorithm for minimizing a not necessarily convex quadratic function over integer variables. The algorithm is based on lower bounds computed as continuous minima of the objective function over appropriate ellipsoids. In the nonconvex case, we use ellipsoids enclosing the feasible region of the problem. In spite of the nonconvexity, these minima can be computed quickly; the corresponding optimization problems are equivalent to trust-region subproblems. We present several ideas that allow us to accelerate the solution of the continuous relaxation within a branch-and-bound scheme and examine the performance of the overall algorithm by computational experiments. Good computational performance is shown especially for ternary instances. © 2013 Society for Industrial and Applied Mathematics.

An exact algorithm for nonconvex quadratic integer minimization using ellipsoidal relaxations / C., Buchheim; DE SANTIS, Marianna; Palagi, Laura; Piacentini, Mauro. - In: SIAM JOURNAL ON OPTIMIZATION. - ISSN 1052-6234. - STAMPA. - 23:3(2013), pp. 1867-1889. [10.1137/120878495]

An exact algorithm for nonconvex quadratic integer minimization using ellipsoidal relaxations

DE SANTIS, MARIANNA
;
PALAGI, Laura;PIACENTINI, Mauro
2013

Abstract

We propose a branch-and-bound algorithm for minimizing a not necessarily convex quadratic function over integer variables. The algorithm is based on lower bounds computed as continuous minima of the objective function over appropriate ellipsoids. In the nonconvex case, we use ellipsoids enclosing the feasible region of the problem. In spite of the nonconvexity, these minima can be computed quickly; the corresponding optimization problems are equivalent to trust-region subproblems. We present several ideas that allow us to accelerate the solution of the continuous relaxation within a branch-and-bound scheme and examine the performance of the overall algorithm by computational experiments. Good computational performance is shown especially for ternary instances. © 2013 Society for Industrial and Applied Mathematics.
2013
global optimization; integer programming; nonconvex programming; quadratic programming
01 Pubblicazione su rivista::01a Articolo in rivista
An exact algorithm for nonconvex quadratic integer minimization using ellipsoidal relaxations / C., Buchheim; DE SANTIS, Marianna; Palagi, Laura; Piacentini, Mauro. - In: SIAM JOURNAL ON OPTIMIZATION. - ISSN 1052-6234. - STAMPA. - 23:3(2013), pp. 1867-1889. [10.1137/120878495]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/485268
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