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A polyhedral study of nonconvex quadratic programs with box constraints

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Abstract.

By reformulating quadratic programs using necessary optimality conditions, we obtain a linear program with complementarity constraints. For the case where the only constraints are bounds on the variables, we study a relaxation based on a subset of the optimality conditions. By characterizing its convex hull, we obtain a large class of valid inequalities. These inequalities are used in a branch-and-cut scheme, see [13].

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Authors and Affiliations

  1. Mechanical and Industrial Engineering, University of Illinois, 1206 West Green Str., Urbana, IL, 61801, USA

    Dieter Vandenbussche

  2. Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, CA, 30332-0205, USA

    George L. Nemhauser

Authors
  1. Dieter Vandenbussche
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  2. George L. Nemhauser
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Correspondence to Dieter Vandenbussche.

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Mathematics Subject Classification (2000): 90C26, 90C27, 90C20

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Vandenbussche, D., Nemhauser, G. A polyhedral study of nonconvex quadratic programs with box constraints. Math. Program. 102, 531–557 (2005). https://doi.org/10.1007/s10107-004-0549-0

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  • DOI: https://doi.org/10.1007/s10107-004-0549-0

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