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On Linear-Time Algorithms for the Continuous Quadratic Knapsack Problem

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Abstract

We give a linear time algorithm for the continuous quadratic knapsack problem which is simpler than existing methods and competitive in practice. Encouraging computational results are presented for large-scale problems.

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References

  1. Brucker, P.: An O(n) algorithm for quadratic knapsack problems. Oper. Res. Lett. 3, 163–166 (1984)

    Article  MATH  Google Scholar 

  2. Calamai, P.H., Moré, J.J.: Quasi-Newton updates with bounds. SIAM J. Numer. Anal. 24, 1434–1441 (1987)

    Article  MATH  Google Scholar 

  3. Maculan, N., Santiago, C.P., Macambira, E.M., Jardim, M.H.C.: An O(n) algorithm for projecting a vector on the intersection of a hyperplane and a box in R n. J. Optim. Theory Appl. 117, 553–574 (2003)

    Article  MATH  Google Scholar 

  4. Pardalos, P.M., Kovoor, N.: An algorithm for a singly-constrained class of quadratic programs subject to upper and lower bounds. Math. Program. 46, 321–328 (1990)

    Article  MATH  Google Scholar 

  5. Bretthauer, K.M., Shetty, B., Syam, S.: A branch- and bound-algorithm for integer quadratic knapsack problems. ORSA J. Comput. 7, 109–116 (1995)

    MATH  Google Scholar 

  6. Knuth, D.E.: Sorting and Searching, 2nd edn. The Art of Computer Programming, vol. III. Addison–Wesley, Reading (1998)

    Google Scholar 

  7. Kiwiel, K.C.: On Floyd and Rivest’s select algorithm. Theor. Comput. Sci. 347, 214–238 (2005)

    Article  MATH  Google Scholar 

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Correspondence to K. C. Kiwiel.

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Communicated by J.P. Crouzeix.

The author thanks the Associate Editor and an anonymous referee for their helpful comments.

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Kiwiel, K.C. On Linear-Time Algorithms for the Continuous Quadratic Knapsack Problem. J Optim Theory Appl 134, 549–554 (2007). https://doi.org/10.1007/s10957-007-9259-0

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  • DOI: https://doi.org/10.1007/s10957-007-9259-0

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