An exact algorithm for nonconvex quadratic integer minimization using ellipsoidal relaxations

C. Buchheim, M. De Santis, L. Palagi, M. Piacentini

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)1867-1889
Number of pages23
JournalSIAM Journal on Optimization
Issue number3
Publication statusPublished - 2013


  • Global optimization
  • Integer programming
  • Nonconvex programming
  • Quadratic programming

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science


Dive into the research topics of 'An exact algorithm for nonconvex quadratic integer minimization using ellipsoidal relaxations'. Together they form a unique fingerprint.

Cite this