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Variable Fixing Algorithms for the Continuous Quadratic Knapsack Problem

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  • K. C. Kiwiel

    (Systems Research Institute)

Abstract

We study several variations of the Bitran–Hax variable fixing method for the continuous quadratic knapsack problem. We close the gaps in the convergence analysis of several existing methods and provide more efficient versions. We report encouraging computational results for large-scale problems.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:136:y:2008:i:3:d:10.1007_s10957-007-9317-7
    DOI: 10.1007/s10957-007-9317-7
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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. Soren S. Nielsen & Stavros A. Zenios, 1992. "Massively Parallel Algorithms for Singly Constrained Convex Programs," INFORMS Journal on Computing, INFORMS, vol. 4(2), pages 166-181, May.
    3. Gabriel R. Bitran & Arnoldo C. Hax, 1981. "Disaggregation and Resource Allocation Using Convex Knapsack Problems with Bounded Variables," Management Science, INFORMS, vol. 27(4), pages 431-441, April.
    4. Steven Cosares & Dorit S. Hochbaum, 1994. "Strongly Polynomial Algorithms for the Quadratic Transportation Problem with a Fixed Number of Sources," Mathematics of Operations Research, INFORMS, vol. 19(1), pages 94-111, February.
    5. 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.
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    Cited by:

    1. 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.
    2. 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.
    3. Martijn H. H. Schoot Uiterkamp & Marco E. T. Gerards & Johann L. Hurink, 2022. "On a Reduction for a Class of Resource Allocation Problems," INFORMS Journal on Computing, INFORMS, vol. 34(3), pages 1387-1402, May.
    4. Torrealba, E.M.R. & Silva, J.G. & Matioli, L.C. & Kolossoski, O. & Santos, P.S.M., 2022. "Augmented Lagrangian algorithms for solving the continuous nonlinear resource allocation problem," European Journal of Operational Research, Elsevier, vol. 299(1), pages 46-59.
    5. 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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