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Solving discrete zero point problems

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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.

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Authors and Affiliations

  1. Department of Econometrics and Tinbergen Institute, Vrije Universiteit, De Boelelaan 1105, 1081, HV, Amsterdam, The Netherlands

    G. van der Laan

  2. Department of Econometrics & Operations Research and CentER, Tilburg University, P.O. Box 90153, 5000, LE, Tilburg, The Netherlands

    D.A.J.J. Talman

  3. Faculty of Business Administration, Yokohama National University, Yokohama, 240-8501, Japan

    Z. Yang

Authors
  1. G. van der Laan
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  2. D.A.J.J. Talman
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  3. Z. Yang
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Corresponding author

Correspondence to D.A.J.J. Talman.

Additional information

This research was carried out when Gerard van der Laan and Zaifu Yang were visiting the CentER of Tilburg University in the summer of 2004. The visit of Zaifu Yang has been made possible by financial support of CentER and the Netherlands Organization for Scientific Research (NWO). The authors gratefully acknowledge the inspiring and helpful remarks of the referees.

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Laan, G., Talman, D. & Yang, Z. Solving discrete zero point problems. Math. Program. 108, 127–134 (2006). https://doi.org/10.1007/s10107-005-0696-y

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  • DOI: https://doi.org/10.1007/s10107-005-0696-y

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