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Exact Algorithm for the Surrogate Dual of an Integer Programming Problem: Subgradient Method Approach

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  • S.-L. Kim

    (Electronics and Telecommunications Research Institute)

  • S. Kim

    (Korea Advanced Institute of Science and Technology)

Abstract

One of the critical issues in the effective use of surrogate relaxation for an integer programming problem is how to solve the surrogate dual within a reasonable amount of computational time. In this paper, we present an exact and efficient algorithm for solving the surrogate dual of an integer programming problem. Our algorithm follows the approach which Sarin et al. (Ref. 8) introduced in their surrogate dual multiplier search algorithms. The algorithms of Sarin et al. adopt an ad-hoc stopping rule in solving subproblems and cannot guarantee the optimality of the solutions obtained. Our work shows that this heuristic nature can actually be eliminated. Convergence proof for our algorithm is provided. Computational results show the practical applicability of our algorithm.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:96:y:1998:i:2:d:10.1023_a:1022622231801
    DOI: 10.1023/A:1022622231801
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    References listed on IDEAS

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    1. Sanjiv Sarin & Mark H. Karwan & Ronald L. Rardin, 1987. "A new surrogate dual multiplier search procedure," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(3), pages 431-450, June.
    2. Fred Glover, 1975. "Surrogate Constraint Duality in Mathematical Programming," Operations Research, INFORMS, vol. 23(3), pages 434-451, June.
    3. 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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    Cited by:

    1. Alidaee, Bahram, 2014. "Zero duality gap in surrogate constraint optimization: A concise review of models," European Journal of Operational Research, Elsevier, vol. 232(2), pages 241-248.
    2. 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.

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