Mathematical Programming

, Volume 102, Issue 3, pp 559–575 | Cite as

A branch-and-cut algorithm for nonconvex quadratic programs with box constraints



We present the implementation of a branch-and-cut algorithm for bound constrained nonconvex quadratic programs. We use a class of inequalities developed in [12] as cutting planes. We present various branching strategies and compare the algorithm to several other methods to demonstrate its effectiveness.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Balas, E.: Nonconvex quadratic programming via generalized polars. SIAM J. Appl. Math. 28, 335–349 (1975)MATHMathSciNetGoogle Scholar
  2. 2.
    Balas, E., Zemel, E.: An algorithm for large zero-one knapsack problems. Oper. Res. 28, 1130–1154 (1980)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Coleman, T.F., Li, Y.: An interior trust region approach for nonlinear minimization subject to bounds. SIAM J. Optim. 6, 418–445 (1996)MATHMathSciNetGoogle Scholar
  4. 4.
    GAMS Development Corporation: General Algebraic Modeling System, Version 2.50, 1998Google Scholar
  5. 5.
    Hansen, P., Jaumard, B., Ruiz, M., Xiong, J.: Global minimization of indefinite quadratic functions subject to box constraints. Nav. Res. Logist. 40, 373–392 (1993)MATHGoogle Scholar
  6. 6.
    ILOG, Inc.: ILOG CPLEX 7.5, User Manual, 2001Google Scholar
  7. 7.
    Linderoth, J.T., Savelsbergh, M.W.P.: A computational study of search strategies for mixed integer programming. Informs J. Comput. 11, 173–187 (1999)MathSciNetMATHGoogle Scholar
  8. 8.
    Mathworks, Inc.: MATLAB Optimization Toolbox 2.0, 1998Google Scholar
  9. 9.
    Nemhauser, G.L., Savelsbergh, M.W.P., Sigismondi, G.S.: MINTO, a Mixed INTeger Optimizer. Oper. Res. Lett. 15, 47–58 (1994)CrossRefMathSciNetMATHGoogle Scholar
  10. 10.
    Sahinidis, N.V.: BARON: a general purpose global optimization software package. J. Glob. Optim. 8, 201–205 (1996)MathSciNetMATHGoogle Scholar
  11. 11.
    Vandenbussche, D.: Polyhedral Approaches to Solving Nonconvex Quadratic Programs. PhD thesis, School of Industrial and Systems Engineering, Georgia Institute of Technology, 2003Google Scholar
  12. 12.
    Vandenbussche, D., Nemhauser, G.L.: A polyhedral study of nonconvex quadratic programs with box constraints. Technical Report TLI-03-04, Georgia Institute of Technology. Math. Prog. 102, 531–557 (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Mechanical and Industrial EngineeringUniversity of IllinoisUrbanaUSA
  2. 2.Industrial and Systems EngineeringGeorgia Institute of TechnologyAtlantaUSA

Personalised recommendations