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Computing Integral Solutions of Complementarity Problems


Author Info

  • Gerard van der Laan

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

  • Dolf Talman

    (Tilburg University)

  • Zaifu Yang

    (Yokohama National University)


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.

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 05-006/1.

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Date of creation: 10 Jan 2005
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Handle: RePEc:dgr:uvatin:20050006

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Keywords: Discrete set; complementarity problem; algorithm; triangulation;

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  1. Talman, A.J.J. & Laan , G. van der, 1987. "Simplicial approximation of solutions to the nonlinear complementarity problem with lower and upper bounds," Open Access publications from Tilburg University urn:nbn:nl:ui:12-153048, Tilburg University.
  2. Iimura, Takuya, 2003. "A discrete fixed point theorem and its applications," Journal of Mathematical Economics, Elsevier, vol. 39(7), pages 725-742, September.
  3. C. E. Lemke, 1965. "Bimatrix Equilibrium Points and Mathematical Programming," Management Science, INFORMS, vol. 11(7), pages 681-689, May.
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Cited by:
  1. Laan, G. van der & Talman, A.J.J. & Yang, Z.F., 2007. "A vector labeling method for solving discrete zero point and complementarity problems," Open Access publications from Tilburg University urn:nbn:nl:ui:12-284192, Tilburg University.
  2. Gerard van der Laan & Dolf Talman & Zaifu Yang, 2009. "Solving Discrete Systems of Nonlinear Equations," Tinbergen Institute Discussion Papers 09-062/1, Tinbergen Institute.
  3. Talman, A.J.J. & Yang, Z.F., 2006. "A Discrete Multivariate Mean Value Theorem with Applications," Discussion Paper 2006-106, Tilburg University, Center for Economic Research.
  4. Laan, G. van der & Talman, A.J.J. & Yang, Z.F., 2011. "Solving discrete systems of nonlinear equations," Open Access publications from Tilburg University urn:nbn:nl:ui:12-4839550, Tilburg University.
  5. 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.
  6. Gerard van der Laan & Dolf Talman & Zaifu Yang, 2007. "Combinatorial Integer Labeling Theorems on Finite Sets with an Application to Discrete Systems of Nonlinear Equations," Tinbergen Institute Discussion Papers 07-084/1, Tinbergen Institute.
  7. Laan, G. van der & Talman, A.J.J. & Yang, Z.F., 2010. "Combinatorial integer labeling theorems on finite sets with applications," Open Access publications from Tilburg University urn:nbn:nl:ui:12-3764045, Tilburg University.


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