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An Exact Algorithm for Quadratic Integer Minimization using Nonconvex Relaxations

Author

Listed:
  • Christoph Buchheim

    (Fakultat fur Mathematik, TU Dortmund)

  • Marianna De Santis

    (Istituto di Analisi dei Sistemi e Informatica Antonio Ruberti – IASI CNR Roma)

  • Laura Palagi

    (Department of Computer, Control, and Management Engineering Antonio Ruberti Sapienza Universita di Roma)

  • Mauro Piacentini

    (Department of Computer, Control, and Management Engineering Antonio Ruberti Sapienza Universita di Roma)

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.

Suggested Citation

  • Christoph Buchheim & Marianna De Santis & Laura Palagi & Mauro Piacentini, 2012. "An Exact Algorithm for Quadratic Integer Minimization using Nonconvex Relaxations," DIS Technical Reports 2012-05, Department of Computer, Control and Management Engineering, Universita' degli Studi di Roma "La Sapienza".
    • Handle: RePEc:aeg:wpaper:2012-5
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    File URL: http://www.dis.uniroma1.it/~bibdis/RePEc/aeg/wpaper/2012-05.pdf
    File Function: First version, 2012
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    References listed on IDEAS

    as
    1. Laura Palagi & Veronica Piccialli & Franz Rendl & Giovanni Rinaldi & Angelika Wiegele, 2012. "Computational Approaches to Max-Cut," International Series in Operations Research & Management Science, in: Miguel F. Anjos & Jean B. Lasserre (ed.), Handbook on Semidefinite, Conic and Polynomial Optimization, chapter 0, pages 821-847, Springer.
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    Cited by:

    1. Christoph Buchheim & Emiliano Traversi, 2018. "Quadratic Combinatorial Optimization Using Separable Underestimators," INFORMS Journal on Computing, INFORMS, vol. 30(3), pages 424-437, August.

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