An analysis of zero set and global error bound properties of a piecewise affine function via its recession function

For a piecewise affine function f : R(n) --> R(m), the recession function is d f(infinity)(x) := (lambda --> infinity) lim f(lambda x)/lambda. In this paper, we study the zero set and error bound properties of f via f(infinity). We show, for example, that f has a zero when f(infinity) has ii unique zero (at the origin) with a nonvanishing index. We also characterize the global error bound property of a piecewise affine function in terms of the recession cones of the zero sets of the function and its recession function.