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Solving Discrete Zero Point Problems with Vector Labeling

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Author Info
Gerard van der Laan () (Faculty of Economics and Business Administration, Vrije Universiteit Amsterdam)
Dolf Talman () (Department of Econometrics & Operations Research, and CentER, Tilburg University)
Zaifu Yang () (Faculty of Business Administration, Yokohama University)

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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 adept the algorithm to prove the existence of a solution to the discrete complementarity problem.

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Publisher Info
Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 05-106/1.

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Date of creation: 28 Nov 2005
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Handle: RePEc:dgr:uvatin:20050106

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Related research
Keywords: integer lattice; zero point; vector labeling rule; simplicial algorithm; Borsuk-Ulam; discrete complementarity;

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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

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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. 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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