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Solving discrete zero point problems

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  • Laan, G. van der
  • Talman, A.J.J.
  • Yang, Z.F.

    (Tilburg University, Center for Economic Research)

Abstract

In this paper an algorithm is proposed to .nd a discrete zero point of a function on the collection of integral points in the n-dimensional Euclidean space IRn.Starting with a given integral point, the algorithm generates a .nite sequence of adjacent integral simplices of varying dimension and terminates with, under certain convergency conditions, a vertex, which yields a discrete zero point of the function under consideration.

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Bibliographic Info

Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2004-113.

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Date of creation: 2004
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Handle: RePEc:dgr:kubcen:2004113

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Related research

Keywords: discrete zero point; discrete fixed point; simplicial algorithm; triangulation;

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References

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  1. Iimura, Takuya, 2003. "A discrete fixed point theorem and its applications," Journal of Mathematical Economics, Elsevier, vol. 39(7), pages 725-742, September.
  2. Herbert E. Scarf, 1967. "The Approximation of Fixed Points of a Continuous Mapping," Cowles Foundation Discussion Papers 216R, Cowles Foundation for Research in Economics, Yale University.
  3. van der Laan, Gerard & Talman, Dolf & Yang, Zaifu, 2002. "Existence and Welfare Properties of Equilibrium in an Exchange Economy with Multiple Divisible and Indivisible Commodities and Linear Production Technologies," Journal of Economic Theory, Elsevier, vol. 103(2), pages 411-428, April.
  4. Talman, A.J.J. & Laan, G. van der, 1979. "A restart algorithm for computing fixed points without an extra dimension," Open Access publications from Tilburg University urn:nbn:nl:ui:12-153012, Tilburg University.
  5. Laan, G. van der & Talman, A.J.J. & Yang, Z.F., 2002. "Existence and welfare properties of equilibrium in an exchange economy with multiple divisible and indivisible commodities and linear production," Open Access publications from Tilburg University urn:nbn:nl:ui:12-89376, Tilburg University.
  6. Scarf, Herbert E, 1981. "Production Sets with Indivisibilities-Part I: Generalities," Econometrica, Econometric Society, vol. 49(1), pages 1-32, January.
  7. Yang, Zaifu, 2000. "Equilibrium in an exchange economy with multiple indivisible commodities and money," Journal of Mathematical Economics, Elsevier, vol. 33(3), pages 353-365, April.
  8. Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, vol. 50(6), pages 1483-1504, November.
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Citations

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Cited by:
  1. Laan, G. van der & Talman, A.J.J. & Yang, Z.F., 2005. "Solving Discrete Zero Point Problems with Vector Labeling," Discussion Paper 2005-122, Tilburg University, Center for Economic Research.
  2. 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.
  3. 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.
  4. 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.
  5. 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.
  6. Laan, G. van der & 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.

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