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Enumeration Approach for Linear Complementarity Problems Based on a Reformulation-Linearization Technique

Author

Listed:
  • H. D. Sherali

    (Virginia Polytechnic Institute and State University)

  • R. S. Krishnamurthy

    (SABRE Technology Solutions)

  • F. A. Al-Khayyal

    (Georgia Institute of Technology)

Abstract

In this paper, we consider the linear complementarity problem (LCP) and present a global optimization algorithm based on an application of the reformulation-linearization technique (RLT). The matrix M associated with the LCP is not assumed to possess any special structure. In this approach, the LCP is formulated first as a mixed-integer 0–1 bilinear programming problem. The RLT scheme is then used to derive a new equivalent mixed-integer linear programming formulation of the LCP. An implicit enumeration scheme is developed that uses Lagrangian relaxation, strongest surrogate and strengthened cutting planes, and a heuristic, designed to exploit the strength of the resulting linearization. Computational experience on various test problems is presented.

Suggested Citation

  • H. D. Sherali & R. S. Krishnamurthy & F. A. Al-Khayyal, 1998. "Enumeration Approach for Linear Complementarity Problems Based on a Reformulation-Linearization Technique," Journal of Optimization Theory and Applications, Springer, vol. 99(2), pages 481-507, November.
    • Handle: RePEc:spr:joptap:v:99:y:1998:i:2:d:10.1023_a:1021734613201
    DOI: 10.1023/A:1021734613201
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    References listed on IDEAS

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    1. B. Curtis Eaves, 1971. "The Linear Complementarity Problem," Management Science, INFORMS, vol. 17(9), pages 612-634, May.
    2. Ronald L. Rardin & V. E. Unger, 1976. "Technical Note—Surrogate Constraints and the Strength of Bounds Derived from 0-1 Benders' Partitioning Procedures," Operations Research, INFORMS, vol. 24(6), pages 1169-1175, December.
    3. M. Seetharama Gowda & Jong-Shi Pang, 1992. "On Solution Stability of the Linear Complementarity Problem," Mathematics of Operations Research, INFORMS, vol. 17(1), pages 77-83, February.
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    Cited by:

    1. Joaquim Júdice, 2012. "Algorithms for linear programming with linear complementarity constraints," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(1), pages 4-25, April.
    2. Warren Adams & Hanif Sherali, 2005. "A Hierarchy of Relaxations Leading to the Convex Hull Representation for General Discrete Optimization Problems," Annals of Operations Research, Springer, vol. 140(1), pages 21-47, November.
    3. Trang T. Nguyen & Jean-Philippe P. Richard & Mohit Tawarmalani, 2021. "Convexification techniques for linear complementarity constraints," Journal of Global Optimization, Springer, vol. 80(2), pages 249-286, June.
    4. Hoai Le Thi & Tao Pham Dinh, 2011. "On solving Linear Complementarity Problems by DC programming and DCA," Computational Optimization and Applications, Springer, vol. 50(3), pages 507-524, December.

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