Normal maps induced by linear transformations

The paper studies a certain piecewise linear manifold, which is called the normal manifold, associated with a polyhedral convex set, and a family of continuous functions, called normal maps, that are induced on this manifold by continuous functions from Rⁿ to Rⁿ. These normal maps occur frequently in optimization and equilibrium problems, and the subclass of normal maps induced by linear transformations plays a key role. The main result is that the normal map induced by a linear álinear transformations plays a key r