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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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    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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