Skip to main content
Springer Nature Link
Log in

A new algorithm for the general quadratic programming problems with box constraints

  • Original Paper
  • Published:
Numerical Algorithms Aims and scope Submit manuscript

Abstract

In this paper, we propose a new branch-and-bound algorithm for the general quadratic problems with box constraints. We, first, transform the problem into a separable form by D. C. decomposition and Cholesky factorization of a positive definite matrix. Then a lower bounding technique is derived and a branch-and-bound algorithm is presented based on the lower bounding and rectangular bisection. Finally, preliminary computational results are reported.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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. Bajirov, A.M., Rubinov, A.M.: Global optimization of marginal functions with applications to economic equilibrium. J. Glob. Optim. 20, 215–237 (2001)

    Article  Google Scholar 

  2. Coleman, T.F., Hulbert, L.A.: A direct active set algorithm for large sparse quadratic programs with simple bounds. Math. Program. 45, 373–406 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  3. De Angelis, P.L., Pardalos, P.M., Toraldo, G.: Quadratic programming with box constraints. In: Bomze, I.M., et al. (eds.) Developments in Global Optimization. Kluwer Academic, Dordrecht (1997)

    Google Scholar 

  4. Hansen, P., Jaumard, B., Ruiz, M., Xiong, J.: Global minimization of indefinite quadratic functions subject to box constraints. Nav. Res. Logist. Q. 40, 373–392 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  5. Horst, R., Pardalos, P.M., Thoai, N.V.: Introduction to Global Optimization. Kluwer Academic, Dordrecht (1995)

    MATH  Google Scholar 

  6. Konnoc, H.: Portfolio optimization problem under concave transaction costs and minimal transaction unit constraints. Math. Program. 89, 233–250 (2001)

    Article  MathSciNet  Google Scholar 

  7. Pardalos, P.M., Vavasis, S.A.: Quadratic programming with one negative eigenvalue is np-hard. J. Glob. Optim. 1, 15–22 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  8. Sherali, H.D., Smith, E.P.: A global optimization approach to a water distribution network design problem. J. Glob. Optim. 11, 107–132 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  9. Le Thi, H.A., Pham Dinh, T.: Solving a class of linearly constrained indefinite quadratic problems by d.c. algorithm. J. Glob. Optim. 11, 253–285 (1997)

    Article  MATH  Google Scholar 

  10. Le Thi, H.A., Pham Dinh, T.: A branch and bound method via d.c. optimization algorithms and ellipsoidal technique for box constrainednonconvex quadratic problems. J. Glob. Optim. 13, 171–206 (1998)

    Article  MATH  Google Scholar 

  11. Vandenbussche, D., Nemhauser, G.L.: A branch-and-cut algorithm for nonconvex quadratic programs with box constraints. Math. Program. Ser. A (2004)

  12. Vavasis, S.A.: Approximate algorithms for indefinite quadratic programming. Math. Program. 57, 279–311 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  13. Yajima, Y., Fujie, T.: A polyhedral approach for nonconvex quadratic progrmming problems with box constraints. J. Glob. Optim. 13, 151–170 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  14. Ye, Y.: On the affine scaling algorithm for nonconvex quadratic programming. Math. Program. 56, 285–300 (1992)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi, 530004, China

    Jianling Li & Lin Ma

  2. Department of Basic Course, Haikou College of Economics, Wentan Road 2, Haikou, Hainan, 570203, China

    Peng Wang

Authors
  1. Jianling Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Peng Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Lin Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jianling Li.

Additional information

This work was supported by National Natural Science Foundation of China under grants 10771040, Guangxi Science Foundation (No. 0728006), the Scientific Research Foundation of Guangxi University (No. X081016) of China.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Li, J., Wang, P. & Ma, L. A new algorithm for the general quadratic programming problems with box constraints. Numer Algor 55, 79–85 (2010). https://doi.org/10.1007/s11075-009-9358-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11075-009-9358-0

Keywords

AMS 2000 Subject Classifications