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A Trust Region Method for the Solution of the Surrogate Dual in Integer Programming

Author

Listed:
  • N. Boland

    (University of Newcastle)

  • A. C. Eberhard

    (RMIT)

  • A. Tsoukalas

    (RMIT)

Abstract

We propose an algorithm for solving the surrogate dual of a mixed integer program. The algorithm uses a trust region method based on a piecewise affine model of the dual surrogate value function. A new and much more flexible way of updating bounds on the surrogate dual’s value is proposed, in which numerical experiments prove to be advantageous. A proof of convergence is given and numerical tests show that the method performance is better than a state of the art subgradient solver. Incorporation of the surrogate dual value as a cut added to the integer program is shown to greatly reduce solution times of a standard commercial solver on a specific class of problems.

Suggested Citation

  • N. Boland & A. C. Eberhard & A. Tsoukalas, 2015. "A Trust Region Method for the Solution of the Surrogate Dual in Integer Programming," Journal of Optimization Theory and Applications, Springer, vol. 167(2), pages 558-584, November.
    • Handle: RePEc:spr:joptap:v:167:y:2015:i:2:d:10.1007_s10957-014-0681-9
    DOI: 10.1007/s10957-014-0681-9
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    References listed on IDEAS

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    1. Sarin, Sanjiv & Karwan, Mark H. & Rardin, Ronald L., 1988. "Surrogate duality in a branch-and-bound procedure for integer programming," European Journal of Operational Research, Elsevier, vol. 33(3), pages 326-333, February.
    2. Duan Li & Xiaoling Sun, 2006. "Nonlinear Integer Programming," International Series in Operations Research and Management Science, Springer, number 978-0-387-32995-6, January.
    3. S.-L. Kim & S. Kim, 1998. "Exact Algorithm for the Surrogate Dual of an Integer Programming Problem: Subgradient Method Approach," Journal of Optimization Theory and Applications, Springer, vol. 96(2), pages 363-375, February.
    4. Harvey J. Greenberg & William P. Pierskalla, 1970. "Surrogate Mathematical Programming," Operations Research, INFORMS, vol. 18(5), pages 924-939, October.
    5. Mark H. Karwan & Ronald L. Rardin, 1984. "Surrogate Dual Multiplier Search Procedures in Integer Programming," Operations Research, INFORMS, vol. 32(1), pages 52-69, February.
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