Solving Discrete Zero Point Problems with Vector Labeling

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