Solving Discrete Zero Point Problems with Vector Labeling

Gerard van der Laan, Adolphus Talman and Zaifu Yang

No 05-106/1, Tinbergen Institute Discussion Papers from Tinbergen Institute

Abstract: This discussion paper resulted in a publication in the 'SIAM Journal on Optimization', 2007, 18, 290-308.

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.

Keywords: integer lattice; zero point; vector labeling rule; simplicial algorithm; Borsuk-Ulam; discrete complementarity (search for similar items in EconPapers)
JEL-codes: C58 C61 C62 C68 C72 (search for similar items in EconPapers)
Date: 2005-11-28
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
https://papers.tinbergen.nl/05106.pdf (application/pdf)

Related works:
Working Paper: Solving Discrete Zero Point Problems with Vector Labeling (2005)
Working Paper: Solving Discrete Zero Point Problems with Vector Labeling (2005)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:tin:wpaper:20050106

Access Statistics for this paper

More papers in Tinbergen Institute Discussion Papers from Tinbergen Institute Contact information at EDIRC.
Bibliographic data for series maintained by Tinbergen Office +31 (0)10-4088900 ().