Ms. Gowda, AN ANALYSIS OF ZERO-SET AND GLOBAL ERROR BOUND PROPERTIES OF A PIECEWISE AFFINE FUNCTION VIA ITS RECESSION FUNCTION, SIAM journal on matrix analysis and applications, 17(3), 1996, pp. 594-609
For a piecewise affine function f : R(n) --> R(m), the recession funct
ion is defined by f(infinity)(x) := (lambda --> infinity) lim f(lambda
x)/lambda. In this paper, we study the zero set and error bound prope
rties of f via f(infinity). We show, for example, that f has a zero wh
en f(infinity) has ii unique zero (at the origin) with a nonvanishing
index. We also characterize the global error bound property of a piece
wise affine function in terms of the recession cones of the zero sets
of the function and its recession function.