Solving discrete zero point problems

  • Authors:

  • G. van der Laan;D. A. J. J. Talman;Z. Yang

  • Affiliations:

  • Department of Econometrics and Tinbergen Institute, Vrije Universiteit, De Boelelaan 1105, 1081, Amsterdam, HV, The Netherlands;Department of Econometrics & Operations Research and CentER, Tilburg University, P.O. Box 90153, De Boelelaan 1105, 5000, Tilburg, LE, The Netherlands;Faculty of Business Administration, Yokohama National University, P.O. Box 90153, De Boelelaan 1105, 240-8501, Yokohama, LE, Japan

  • Venue:
  • Mathematical Programming: Series A and B
  • Year:
  • 2006

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Abstract

In this paper we present two theorems 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. The theorems differ in their boundary conditions. For both theorems we give a proof using a combinatorial lemma and present a constructive proof based on a simplicial algorithm that finds a discrete zero point within a finite number of steps.