Skip to main content
Springer Nature Link
Log in

An algorithm for a singly constrained class of quadratic programs subject to upper and lower bounds

  • Published:
Mathematical Programming Submit manuscript

Abstract

This paper gives an O(n) algorithm for a singly constrained convex quadratic program using binary search to solve the Kuhn-Tucker system. Computational results indicate that a randomized version of this algorithm runs in expected linear time and is suitable for practical applications. For the nonconvex case anε-approximate algorithm is proposed which is based on convex and piecewise linear approximations of the objective function.

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. A.V. Aho, J.E. Hopcroft and J.D. Ullman,The Design and Analysis of Computer Algorithms (Addison-Wesley, Reading, MA, 1974).

    Google Scholar 

  2. M.R. Blum, R.W. Floyd, V.R. Pratt, R.L. Rivest and R.E. Tarjan, “Time bounds for selection,”Journal of Computer and System Sciences 7(4) (1972) 448–461.

    Google Scholar 

  3. P. Brucker, “An O(n) algorithm for quadratic knapsack problems,”Operations Research Letters 3 (1984) 163–166.

    Google Scholar 

  4. P.H. Calamai and J.J. Moré, “Quasi-Newton updates with bounds,”SIAM Journal on Numerical Analysis 24 (1987) 1434–1441.

    Google Scholar 

  5. N.J. Driebeek, “An algorithm for the solution of mixed integer programming problems,”Management Science 12 (1966) 576–587.

    Google Scholar 

  6. A.M. Geoffrion and R.E. Marsten, “Integer programming algorithms: A framework and state of the art survey,”Management Science 18 (1972) 465–491.

    Google Scholar 

  7. M. Held, P. Wolfe and H. Crowder, “Validation of subgradient optimization,”Mathematical Programming 6 (1974) 62–88.

    Google Scholar 

  8. R. Helgason, J. Kennington and H. Lall, “A polynomially bounded algorithm for a singly constrained quadratic program,”Mathematical Programming 18 (1980) 338–343.

    Google Scholar 

  9. R.R. Meyer, “Multipoint methods for separable nonlinear networks,”Mathematical Programming Study 22 (1984) 185–205.

    Google Scholar 

  10. P.M. Pardalos and J.B. Rosen, “Constrained global optimization: Algorithms and applications,” in:Lecture Notes in Computer Science, Vol. 268 (Springer, Berlin, 1987).

    Google Scholar 

  11. P.M. Pardalos and J.B. Rosen, “Methods for global concave minimization: A bibliographic survey,”SIAM Review 28(3) (1986) 367–379.

    Google Scholar 

  12. J.B. Rosen and P.M. Pardalos, “Global minimization of large-scale constrained concave quadratic problems by separable programming,”Mathematical Programming 34 (1986) 163–174.

    Google Scholar 

  13. L. Schrage,Linear Integer and Quadratic Programming with LINDO (Scientific Press, Palo Alto, CA, 1984).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Computer Science Department, The Pennsylvania State University, 16802, University Park, PA, USA

    P. M. Pardalos & N. Kovoor

Authors
  1. P. M. Pardalos
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. N. Kovoor
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pardalos, P.M., Kovoor, N. An algorithm for a singly constrained class of quadratic programs subject to upper and lower bounds. Mathematical Programming 46, 321–328 (1990). https://doi.org/10.1007/BF01585748

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01585748

Key words