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Solving discrete zero point problems with vector labeling

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Author Info
Laan, Gerard van der
Talman, Dolf
Yang, Zaifu (Tilburg University, Center for Economic Research)

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Abstract

In this paper we present two general results on the existence of a discrete zero point of a function from the n-dimensional integer lattice Zn to the n-dimensional Euclidean space Rn. Under two different boundary conditions, we give a constructive proof using a combinatorial argument based on a simplicial algorithm with vector labeling and lexicographic linear programming pivot steps. We also adapt the algorithm to prove the existence of a solution to the discrete complementarity problem.

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Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 122.

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Date of creation: 2005
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Handle: RePEc:dgr:kubcen:2005122

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Web page: http://center.uvt.nl

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Related research
Keywords: zero point; vector labeling rule; simplicial algorithm; Borsuk-Ulam; discrete complementarity; 47H10; 54H25; 55M20; 90C26; 90C33; 91B50; integer lattices;

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Find related papers by JEL classification:
C61 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Optimization Techniques; Programming Models; Dynamic Analysis
C62 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Existence and Stability Conditions of Equilibrium
C68 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Computable General Equilibrium Models
C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
C68 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Computable General Equilibrium Models

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  1. Herbert E. Scarf, 1967. "The Approximation of Fixed Points of a Continuous Mapping," Cowles Foundation Discussion Papers 216R, Cowles Foundation, Yale University. [Downloadable!]
  2. Gerard van der Laan & Dolf Talman & Zaifu Yang, 2005. "Computing Integral Solutions of Complementarity Problems," Tinbergen Institute Discussion Papers 05-006/1, Tinbergen Institute. [Downloadable!]
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  3. Iimura, Takuya, 2003. "A discrete fixed point theorem and its applications," Journal of Mathematical Economics, Elsevier, vol. 39(7), pages 725-742, September. [Downloadable!] (restricted)
  4. Laan, G. van der & Talman, A.J.J. & Yang, Z., 2004. "Solving discrete zero point problems," Discussion Paper 113, Tilburg University, Center for Economic Research. [Downloadable!]
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Talman, Dolf & Yang, Zaifu, 2006. "A discrete multivariate mean value theorem with applications," Discussion Paper 106, Tilburg University, Center for Economic Research. [Downloadable!]
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