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A new surrogate dual multiplier search procedure

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  • Sanjiv Sarin
  • Mark H. Karwan
  • Ronald L. Rardin

Abstract

Efficient computation of tight bounds is of primary concern in any branch‐and‐bound procedure for solving integer programming problems. Many successful branch‐and‐bound approaches use the linear programming relaxation for bounding purposes. Significant interest has been reported in Lagrangian and surrogate duals as alternative sources of bounds. The existence of efficient techniques such as subgradient search for solving Lagrangian duals has led to some very successful applications of Lagrangian duality in solving specially structured problems. While surrogate duals have been theoretically shown to provide stronger bounds, the difficulty of surrogate dual‐multiplier search has discouraged their employment in solving integer programs. Based on the development of a new relationship between surrogate and Lagrangian duality, we suggest a new strategy for computing surrogate dual values. The proposed approach allows us to directly use established Lagrangian search methods for exploring surrogate dual multipliers. Computational experience with randomly generated capital budgeting problems validates the economic feasibility of the proposed ideas.

Suggested Citation

  • 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.
    • Handle: RePEc:wly:navres:v:34:y:1987:i:3:p:431-450
    DOI: 10.1002/1520-6750(198706)34:33.0.CO;2-P
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    References listed on IDEAS

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    1. Marshall L. Fisher, 1981. "The Lagrangian Relaxation Method for Solving Integer Programming Problems," Management Science, INFORMS, vol. 27(1), pages 1-18, January.
    2. Fred Glover, 1975. "Surrogate Constraint Duality in Mathematical Programming," Operations Research, INFORMS, vol. 23(3), pages 434-451, June.
    3. A. M. Geoffrion, 1969. "An Improved Implicit Enumeration Approach for Integer Programming," Operations Research, INFORMS, vol. 17(3), pages 437-454, June.
    4. Mark H. Karwan & Ronald L. Rardin, 1981. "Surrogate duality in a branch‐and‐bound procedure," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 28(1), pages 93-101, March.
    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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    Cited by:

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    2. 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.
    3. Yuji Nakagawa & Ross J. W. James & César Rego & Chanaka Edirisinghe, 2014. "Entropy-Based Optimization of Nonlinear Separable Discrete Decision Models," Management Science, INFORMS, vol. 60(3), pages 695-707, March.

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