Solutions to Affine Generalized Equations Using Proximal Mappings

Abstract

The normal map has proven to be a powerful tool for solving generalized equations of the form: find z ? C, with 0 ? F(z)+ Nc(z), where C is a convex set and Nc(z) is the normal cone to C at z. In this paper, we use the T-map, a generalization of the normal map, to solve equations of the more general form: find z ? dom(T), with 0 ? F(z) + T(z), where T is a maximal monotone multifunction. We present a path-following algorithm that determines zeros of coherently oriented piecewise-affine functions, and we use this algorithm, together with the T-map, to solve the generalized equation for affine, coherently oriented functions F, and polyhedral multifunctions T.