A new proof of Robinson's homeomorphism theorem for pl-normal maps

Abstract

We study a certain class of piecewise linear functions from R n to R n , namely Robinson's normal maps induced by linear mappings and polyhedral convex sets, called pl-normal maps. Robinson's homeomorphism theorem characterizes the pl- normal maps which are homeomorphisms as those which have nonzero determinants of the same sign on all pieces of linearity. This paper presents a new shorter proof of the result. Pl-normal systems include many optimization and equilibrium problems. They arise from variational inequalities, or equivalently generalized equations, specified by linear maps and polyhedral convex sets. Unique, continuous solvability of these systems, which is important in theory and computation, is captured by the homeomorphism result.