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Globally solving nonconvex quadratic programming problems via completely positive programming

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Abstract

Nonconvex quadratic programming (QP) is an NP-hard problem that optimizes a general quadratic function over linear constraints. This paper introduces a new global optimization algorithm for this problem, which combines two ideas from the literature—finite branching based on the first-order KKT conditions and polyhedral-semidefinite relaxations of completely positive (or copositive) programs. Through a series of computational experiments comparing the new algorithm with existing codes on a diverse set of test instances, we demonstrate that the new algorithm is an attractive method for globally solving nonconvex QP.

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Authors and Affiliations

  1. Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL, 60439, USA

    Jieqiu Chen

  2. Department of Management Sciences, University of Iowa, Iowa City, IA, 52242-1994, USA

    Samuel Burer

Authors
  1. Jieqiu Chen
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  2. Samuel Burer
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Correspondence to Jieqiu Chen.

Additional information

The submitted manuscript has been created by the UChicago Argonne, LLC, Operator of Argonne National Laboratory (“Argonne”) under Contract No. DE-AC02-06CH11357 with the U.S. Department of Energy. The U.S. Government retains for itself, and others acting on its behalf, a paid-up, nonexclusive, irrevocable worldwide license in said article to reproduce, prepare derivative works, distribute copies to the public, and perform publicly and display publicly, by or on behalf of the Government.

The research of J. Chen and S. Burer was supported in part by NSF Grant CCF-0545514. J. Chen was supported in part by the Office of Advanced Scientific Computing Research, Office of Science, U.S. Department of Energy, under Contract DE-AC02-06CH11357.

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Chen, J., Burer, S. Globally solving nonconvex quadratic programming problems via completely positive programming. Math. Prog. Comp. 4, 33–52 (2012). https://doi.org/10.1007/s12532-011-0033-9

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  • DOI: https://doi.org/10.1007/s12532-011-0033-9

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