A polyhedral study of nonconvex quadratic programs with box constraints

Authors:
Dieter Vandenbussche;George L. Nemhauser
Affiliations:
University of Illinois, Mechanical and Industrial Engineering, 1206 West Green Str., 61801, Urbana, IL, USA;Georgia Institute of Technology, Industrial and Systems Engineering, 1206 West Green Str., 30332-0205, Atlanta, CA, USA
Venue:
Mathematical Programming: Series A and B
Year:
2005

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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].