A New Constructive Proof to the Ezistence of an Integer Zero Point of a Mapping with the Direction Preserving Property
Let f: Zn→Rn be a mapping satisfying the direction preserving property that fi(x)>0 implies fi(y)≥0 for any integer points x and y with ‖x-y‖∞≤1. We assume that there is an integer point xo with c≤xo≤d satisfying that max1≤i≤n(xi-xoi)fi(x)＞0 for any integer point x with f(x)≠0 on the boundary of H=x∈Rn∣c-e≤x≤d+e, where c and d are two finite integer points with c≤d and e=(1.1,……, 1) (T) ∈Rn. This assumption is implied by one of two different conditions for the existence of an integer zero point of the mapping in van der Laan et al. (2004). Under the assumption, there is an integer point x*∈H such that f(x*)=0. A constructive proof of the existence is derived from an application of the well-known (n+1)-ray algorithm for computing a fixed point. The existence result has applications in general equilibrium models with indivisible commodities.
Integer Zero Point Direction Preserving Simplicial Algorithm Triangulation Ezistence
Chuangyin Dang Guixian Zhong
Dept. of Manufacturing Engineering & Engineering Management City University of Hong Kong, Kowloon, Hong Kong
国际会议
张家界
英文
90-96
2009-09-20（万方平台首次上网日期，不代表论文的发表时间）