Skip to main content
SpringerLink
Log in

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

  • Published:
Mathematical Programming Submit manuscript

Abstract.

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Balas, E.: Nonconvex quadratic programming via generalized polars. SIAM J. Appl. Math. 28, 335–349 (1975)

    MATH  MathSciNet  Google Scholar 

  2. Balas, E., Zemel, E.: An algorithm for large zero-one knapsack problems. Oper. Res. 28, 1130–1154 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  3. Coleman, T.F., Li, Y.: An interior trust region approach for nonlinear minimization subject to bounds. SIAM J. Optim. 6, 418–445 (1996)

    MATH  MathSciNet  Google Scholar 

  4. GAMS Development Corporation: General Algebraic Modeling System, Version 2.50, 1998

  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)

    MATH  Google Scholar 

  6. ILOG, Inc.: ILOG CPLEX 7.5, User Manual, 2001

  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)

    MathSciNet  MATH  Google Scholar 

  8. Mathworks, Inc.: MATLAB Optimization Toolbox 2.0, 1998

  9. Nemhauser, G.L., Savelsbergh, M.W.P., Sigismondi, G.S.: MINTO, a Mixed INTeger Optimizer. Oper. Res. Lett. 15, 47–58 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  10. Sahinidis, N.V.: BARON: a general purpose global optimization software package. J. Glob. Optim. 8, 201–205 (1996)

    MathSciNet  MATH  Google Scholar 

  11. Vandenbussche, D.: Polyhedral Approaches to Solving Nonconvex Quadratic Programs. PhD thesis, School of Industrial and Systems Engineering, Georgia Institute of Technology, 2003

  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)

Download references

Author information

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, GA, 30332-0205, USA

    George L. Nemhauser

Authors
  1. Dieter Vandenbussche
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. George L. Nemhauser
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dieter Vandenbussche.

Additional information

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

Rights and permissions

Reprints and permissions

About this article

Cite this article

Vandenbussche, D., Nemhauser, G. A branch-and-cut algorithm for nonconvex quadratic programs with box constraints. Math. Program. 102, 559–575 (2005). https://doi.org/10.1007/s10107-004-0550-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10107-004-0550-7

Keywords

Search

Navigation