Mathematical Programming

, Volume 46, Issue 1–3, pp 321–328 | Cite as

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

  • P. M. Pardalos
  • N. Kovoor
Article
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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.

Key words

Global optimization separable programming quadratic programming 
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References

  1. [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. [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. [3]
    P. Brucker, “An O(n) algorithm for quadratic knapsack problems,”Operations Research Letters 3 (1984) 163–166.Google Scholar
  4. [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. [5]
    N.J. Driebeek, “An algorithm for the solution of mixed integer programming problems,”Management Science 12 (1966) 576–587.Google Scholar
  6. [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. [7]
    M. Held, P. Wolfe and H. Crowder, “Validation of subgradient optimization,”Mathematical Programming 6 (1974) 62–88.Google Scholar
  8. [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. [9]
    R.R. Meyer, “Multipoint methods for separable nonlinear networks,”Mathematical Programming Study 22 (1984) 185–205.Google Scholar
  10. [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. [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. [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. [13]
    L. Schrage,Linear Integer and Quadratic Programming with LINDO (Scientific Press, Palo Alto, CA, 1984).Google Scholar

Copyright information

© North-Holland 1990

Authors and Affiliations

  • P. M. Pardalos
    • 1
  • N. Kovoor
    • 1
  1. 1.Computer Science DepartmentThe Pennsylvania State UniversityUniversity ParkUSA

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