Solving discrete zero point problems with vector labeling

Gerard van der Laan, Dolf Talman () and Zaifu Yang
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Zaifu Yang: Tilburg University, Center for Economic Research

No 122, Discussion Paper from Tilburg University, Center for Economic Research

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

Keywords: zero point; vector labeling rule; simplicial algorithm; Borsuk-Ulam; discrete complementarity; 47H10; 54H25; 55M20; 90C26; 90C33; 91B50; integer lattices (search for similar items in EconPapers)
JEL-codes: C61 C62 C68 C72 C68 (search for similar items in EconPapers)
Date: 2005
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Working Paper: Solving Discrete Zero Point Problems with Vector Labeling (2005)
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Persistent link: http://EconPapers.repec.org/RePEc:dgr:kubcen:2005122

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