%A Stephen C. Billups
%A Michael C. Ferris
%T Solutions to Affine Generalized Equations using Proximal Mappings
%D November 1994
%R 94-15
%I COMPUTER SCIENCES DEPARTMENT, UNIVERSITY OF WISCONSIN
%C MADISON, WI
%X Robinson's normal map has proven to be a powerful tool for solving
generalized equations of the form: find $z \in C$, with $0 \in F(z) + N_C(z)$,
where $C$ is a convex set and $N_C(z)$ is the normal cone to $C$ at $z$.
In this paper, we introduce the $T$-map, a generalization of the normal
map, which can be used to solve equations of the more general
form: find $z \in \dom(T)$, with $0 \in F(z) + T(z)$, where $T$ is a maximal
monotone multifunction. A path-following algorithm based on the $T$-map
is presented that solves the generalized equation for affine, coherently
oriented $F$, and polyhedral $T$.