Template-Type: ReDIF-Paper 1.0 Series: Tinbergen Institute Discussion Papers Creation-Date: 2005-11-28 Number: 05-106/1 Author-Name: Gerard van der Laan Author-Email: glaan@feweb.vu.nl Author-Workplace-Name: Faculty of Economics and Business Administration, Vrije Universiteit Amsterdam Author-Name: Dolf Talman Author-Email: talman@uvt.nl Author-Workplace-Name: Department of Econometrics & Operations Research, and CentER, Tilburg University Author-Name: Zaifu Yang Author-Email: yang@ynu.ac.jp Author-Workplace-Name: Faculty of Business Administration, Yokohama University Title: Solving Discrete Zero Point Problems with Vector Labeling 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. Classification-JEL: C61; C62; C68; C72; C58 Keywords: integer lattice; zero point; vector labeling rule; simplicial algorithm; Borsuk-Ulam; discrete complementarity File-Url: https://papers.tinbergen.nl/05106.pdf File-Format: application/pdf File-Size: 262608 bytes Handle: RePEc:tin:wpaper:20050106