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An O(n) Algorithm for Projecting a Vector on the Intersection of a Hyperplane and a Box in Rn

Author

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  • N. Maculan

    (Universidade Federal do Rio de Janeiro)

  • C.P. Santiago

    (Universidade Federal do Rio de Janeiro)

  • E.M. Macambira

    (Universidade Federal do Rio de Janeiro)

  • M.H.C. Jardim

    (Universidade Federal do Rio de Janeiro)

Abstract

We consider the problem of projecting a vector on the intersection of a hyperplane and a box in Rn. This paper extends a previous result of Maculan, Minoux, and Plateau (Ref. 1) concerning the projection of a vector on the intersection of a hyperplane and Rn +. We present an O(n) time algorithm based on the linear-time median-finding algorithm. This algorithm determines the median of the components of the vector to be projected. Computational results are also presented in order to evaluate the algorithm and its time complexity. We consider two sets of instances which are randomly generated for any given n. The algorithm was successful in solving all the instances in a reasonable time.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:117:y:2003:i:3:d:10.1023_a:1023997605430
    DOI: 10.1023/A:1023997605430
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    References listed on IDEAS

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    1. Jeff Kennington & Mohamed Shalaby, 1977. "An Effective Subgradient Procedure for Minimal Cost Multicommodity Flow Problems," Management Science, INFORMS, vol. 23(9), pages 994-1004, May.
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    Cited by:

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    2. Aviad Aberdam & Amir Beck, 2022. "An Accelerated Coordinate Gradient Descent Algorithm for Non-separable Composite Optimization," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 219-246, June.
    3. 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.
    4. Le Thi, Hoai An & Ta, Anh Son & Pham Dinh, Tao, 2018. "An efficient DCA based algorithm for power control in large scale wireless networks," Applied Mathematics and Computation, Elsevier, vol. 318(C), pages 215-226.
    5. Patriksson, Michael, 2008. "A survey on the continuous nonlinear resource allocation problem," European Journal of Operational Research, Elsevier, vol. 185(1), pages 1-46, February.

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