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Global Optimization Method for Solving Mathematical Programs with Linear Complementarity Constraints

Author

Listed:
  • N. V. Thoai

    (University of Trier)

  • Y. Yamamoto

    (University of Trier)

  • A. Yoshise

    (University of Trier)

Abstract

We propose a method for finding a global optimal solution of programs with linear complementarity constraints. This problem arises for instance in bilevel programming. The main idea of the method is to generate a sequence of points either ending at a global optimal solution within a finite number of iterations or converging to a global optimal solution. The construction of such sequence is based on branch-and-bound techniques, which have been used successfully in global optimization. Results on a numerical test of the algorithm are reported.

Suggested Citation

  • N. V. Thoai & Y. Yamamoto & A. Yoshise, 2005. "Global Optimization Method for Solving Mathematical Programs with Linear Complementarity Constraints," Journal of Optimization Theory and Applications, Springer, vol. 124(2), pages 467-490, February.
    • Handle: RePEc:spr:joptap:v:124:y:2005:i:2:d:10.1007_s10957-004-0946-9
    DOI: 10.1007/s10957-004-0946-9
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    References listed on IDEAS

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    1. Nguyen Van Thoai & Hoang Tuy, 1980. "Convergent Algorithms for Minimizing a Concave Function," Mathematics of Operations Research, INFORMS, vol. 5(4), pages 556-566, November.
    2. 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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