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An Exact Algorithm for Quadratic Integer Minimization using Ellipsoidal Relaxations

Christoph Buchheim (christoph.buchheim***at***tu-dortmund.de)
Marianna De Santis (mdesantis***at***dis.uniroma1.it)
Laura Palagi (palagi***at***dis.uniroma1.it)
Mauro Piacentini (piacentini***at***dis.uniroma1.it)

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 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.

Keywords: Quadratic integer programming, nonconvex relaxations

Category 1: Integer Programming ((Mixed) Integer Nonlinear Programming )

Category 2: Nonlinear Optimization (Quadratic Programming )

Category 3: Global Optimization (Other )

Citation: SIAM Journal on Optimization, 23(3), pp. 1867-1889, (2013)

Download: [PDF]

Entry Submitted: 05/23/2012
Entry Accepted: 05/23/2012
Entry Last Modified: 07/28/2016

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