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On Linear-Time Algorithms for the Continuous Quadratic Knapsack Problem

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  • K. C. Kiwiel

    (Systems Research Institute)

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.

Suggested Citation

  • K. C. Kiwiel, 2007. "On Linear-Time Algorithms for the Continuous Quadratic Knapsack Problem," Journal of Optimization Theory and Applications, Springer, vol. 134(3), pages 549-554, September.
    • Handle: RePEc:spr:joptap:v:134:y:2007:i:3:d:10.1007_s10957-007-9259-0
    DOI: 10.1007/s10957-007-9259-0
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    References listed on IDEAS

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    1. Kurt M. Bretthauer & Bala Shetty & Siddhartha Syam, 1995. "A Branch and Bound Algorithm for Integer Quadratic Knapsack Problems," INFORMS Journal on Computing, INFORMS, vol. 7(1), pages 109-116, February.
    2. N. Maculan & C.P. Santiago & E.M. Macambira & M.H.C. Jardim, 2003. "An O(n) Algorithm for Projecting a Vector on the Intersection of a Hyperplane and a Box in Rn," Journal of Optimization Theory and Applications, Springer, vol. 117(3), pages 553-574, June.
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    Citations

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    Cited by:

    1. Paul Tseng & Sangwoon Yun, 2010. "A coordinate gradient descent method for linearly constrained smooth optimization and support vector machines training," Computational Optimization and Applications, Springer, vol. 47(2), pages 179-206, October.
    2. Ion Necoara & Andrei Patrascu, 2014. "A random coordinate descent algorithm for optimization problems with composite objective function and linear coupled constraints," Computational Optimization and Applications, Springer, vol. 57(2), pages 307-337, March.
    3. Meijiao Liu & Yong-Jin Liu, 2017. "Fast algorithm for singly linearly constrained quadratic programs with box-like constraints," Computational Optimization and Applications, Springer, vol. 66(2), pages 309-326, March.
    4. Cassioli, A. & Di Lorenzo, D. & Sciandrone, M., 2013. "On the convergence of inexact block coordinate descent methods for constrained optimization," European Journal of Operational Research, Elsevier, vol. 231(2), pages 274-281.
    5. Hsin-Min Sun & Ruey-Lin Sheu, 2019. "Minimum variance allocation among constrained intervals," Journal of Global Optimization, Springer, vol. 74(1), pages 21-44, May.
    6. K. C. Kiwiel, 2008. "Variable Fixing Algorithms for the Continuous Quadratic Knapsack Problem," Journal of Optimization Theory and Applications, Springer, vol. 136(3), pages 445-458, March.
    7. Amir Beck & Nadav Hallak, 2016. "On the Minimization Over Sparse Symmetric Sets: Projections, Optimality Conditions, and Algorithms," Mathematics of Operations Research, INFORMS, vol. 41(1), pages 196-223, February.
    8. P. Tseng & S. Yun, 2009. "Block-Coordinate Gradient Descent Method for Linearly Constrained Nonsmooth Separable Optimization," Journal of Optimization Theory and Applications, Springer, vol. 140(3), pages 513-535, March.
    9. Hoto, R.S.V. & Matioli, L.C. & Santos, P.S.M., 2020. "A penalty algorithm for solving convex separable knapsack problems," Applied Mathematics and Computation, Elsevier, vol. 387(C).

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