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Computing Integral Solutions of Complementarity Problems

Author

Listed:
  • Gerard van der Laan

    (Faculty of Economics and Business Administration, Vrije Universiteit Amsterdam)

  • Dolf Talman

    (Tilburg University)

  • Zaifu Yang

    (Yokohama National University)

Abstract

This discussion paper resulted in a publication in 'Discrete Optimization', 2007, 4, 315-321. In this paper an algorithm is proposed to find an integral solution of (nonlinear) complementarity problems. The algorithm starts with a nonnegative integral point and generates a unique sequence of adjacent integral simplices of varying dimension. Conditions are stated under which the algorithm terminates with a simplex one of whose vertices is an integral solution of the complementarity problem under consideration.

Suggested Citation

  • Gerard van der Laan & Dolf Talman & Zaifu Yang, 2005. "Computing Integral Solutions of Complementarity Problems," Tinbergen Institute Discussion Papers 05-006/1, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20050006
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    References listed on IDEAS

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    1. William H. Cunningham & James F. Geelen, 1998. "Integral Solutions of Linear Complementarity Problems," Mathematics of Operations Research, INFORMS, vol. 23(1), pages 61-68, February.
    2. ,, 2004. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 20(2), pages 427-429, April.
    3. Iimura, Takuya, 2003. "A discrete fixed point theorem and its applications," Journal of Mathematical Economics, Elsevier, vol. 39(7), pages 725-742, September.
    4. ,, 2004. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 20(1), pages 223-229, February.
    5. Iimura, Takuya & Murota, Kazuo & Tamura, Akihisa, 2005. "Discrete fixed point theorem reconsidered," Journal of Mathematical Economics, Elsevier, vol. 41(8), pages 1030-1036, December.
    6. C. E. Lemke, 1965. "Bimatrix Equilibrium Points and Mathematical Programming," Management Science, INFORMS, vol. 11(7), pages 681-689, May.
    7. R. Chandrasekaran & S. N. Kabadi & R. Sridhar, 1998. "Integer Solution for Linear Complementarity Problem," Mathematics of Operations Research, INFORMS, vol. 23(2), pages 390-402, May.
    8. G. van der Laan, 1981. "Simplicial fixed point algorithms," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 35(1), pages 58-58, March.
    9. 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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    Citations

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    Cited by:

    1. Gerard van der Laan & Dolf Talman & Zaifu Yang, 2005. "Solving Discrete Zero Point Problems with Vector Labeling," Tinbergen Institute Discussion Papers 05-106/1, Tinbergen Institute.
    2. van der Laan, G. & Talman, A.J.J. & Yang, Z.F., 2007. "Combinatorial Integer Labeling Thorems on Finite Sets with an Application to Discrete Systems of Nonlinear Equations," Discussion Paper 2007-88, Tilburg University, Center for Economic Research.
    3. Talman, Dolf & Yang, Zaifu, 2009. "A discrete multivariate mean value theorem with applications," European Journal of Operational Research, Elsevier, vol. 192(2), pages 374-381, January.
    4. G. Laan & A. J. J. Talman & Z. Yang, 2010. "Combinatorial Integer Labeling Theorems on Finite Sets with Applications," Journal of Optimization Theory and Applications, Springer, vol. 144(2), pages 391-407, February.
    5. van der Laan, Gerard & Talman, Dolf & Yang, Zaifu, 2011. "Solving discrete systems of nonlinear equations," European Journal of Operational Research, Elsevier, vol. 214(3), pages 493-500, November.
    6. van der Laan, G. & Talman, A.J.J. & Yang, Z.F., 2007. "A vector labeling method for solving discrete zero point and complementarity problems," Other publications TiSEM 070869d0-4e42-4d34-85f9-b, Tilburg University, School of Economics and Management.

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    More about this item

    Keywords

    Discrete set; complementarity problem; algorithm; triangulation;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C68 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computable General Equilibrium Models
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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