An Exact Algorithm for Quadratic Integer Minimization using Nonconvex Relaxations

Authors

  • Christoph Buchheim Fakult¨at f¨ur Mathematik, TU Dortmund
  • Marianna De Santis Istituto di Analisi dei Sistemi e Informatica Antonio Ruberti
  • Laura Palagi Department of Computer, Control, and Management Engineering Antonio Ruberti
  • Mauro Piacentini Department of Computer, Control, and Management Engineering Antonio Ruberti

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. 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.

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How to Cite

Buchheim, C., De Santis, M., Palagi, L., & Piacentini, M. (2012). An Exact Algorithm for Quadratic Integer Minimization using Nonconvex Relaxations. Department of Computer and System Sciences Antonio Ruberti Technical Reports, 4(5), 29. Retrieved from https://rosa.uniroma1.it/rosa00/index.php/dis_technical_reports/article/view/10023

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