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A logarithmic descent direction algorithm for the quadratic knapsack problem

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  • Wu, Zhengtian
  • Jiang, Baoping
  • Karimi, Hamid Reza

Abstract

The quadratic knapsack problem is an NP-hard optimization problem with many diverse applications in industrial and management engineering. However, computational complexities still remain in the quadratic knapsack problem. In this study, a logarithmic descent direction algorithm is proposed to approximate a solution to the quadratic knapsack problem. The proposed algorithm is based on the Karush–Kuhn–Tucker necessary optimality condition and the damped Newton method. The convergence of the algorithm is proven, and the numerical results indicate its effectiveness.

Suggested Citation

  • Wu, Zhengtian & Jiang, Baoping & Karimi, Hamid Reza, 2020. "A logarithmic descent direction algorithm for the quadratic knapsack problem," Applied Mathematics and Computation, Elsevier, vol. 369(C).
    • Handle: RePEc:eee:apmaco:v:369:y:2020:i:c:s009630031930846x
    DOI: 10.1016/j.amc.2019.124854
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    References listed on IDEAS

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    1. Yurii Nesterov, 2018. "Lectures on Convex Optimization," Springer Optimization and Its Applications, Springer, edition 2, number 978-3-319-91578-4, March.
    2. Lai, Xiangjing & Hao, Jin-Kao & Yue, Dong, 2019. "Two-stage solution-based tabu search for the multidemand multidimensional knapsack problem," European Journal of Operational Research, Elsevier, vol. 274(1), pages 35-48.
    3. David Bergman, 2019. "An Exact Algorithm for the Quadratic Multiknapsack Problem with an Application to Event Seating," INFORMS Journal on Computing, INFORMS, vol. 31(3), pages 477-492, July.
    4. Gintaras Palubeckis, 2004. "Multistart Tabu Search Strategies for the Unconstrained Binary Quadratic Optimization Problem," Annals of Operations Research, Springer, vol. 131(1), pages 259-282, October.
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    Cited by:

    1. Elias Munapo & Santosh Kumar, 2021. "Reducing the complexity of the knapsack linear integer problem by reformulation techniques," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 12(6), pages 1087-1093, December.
    2. Yu, Yaolong & Wu, Zhengtian & Jiang, Baoping & Yan, Huaicheng & Lu, Yichen, 2025. "A Lagrange barrier approach for the minimum concave cost supply problem via a logarithmic descent direction algorithm," Applied Mathematics and Computation, Elsevier, vol. 488(C).

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