Name
Abstract | ||
|---|---|---|
The normal map has proven to be a powerful tool for solving generalized equations of the form: find z ∈ C, with 0 ∈ Fz + Ncz, where C is a convex set and Ncz 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 ∈ domT, with 0 ∈ Fz + Tz, 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. The path-following algorithm we develop here extends the piecewise-linear homotopy framework of Eaves to the case where a representation of a subdivided manifold is unknown. |
Year | DOI | Venue |
|---|---|---|
1999 | 10.1287/moor.24.1.219 | Math. Oper. Res. |
Keywords | DocType | Volume |
piecewise affine,path-following algorithm,oriented functions f,convex set,maximal monotone multifunction,piecewise-affine function,general form,affine generalized,homotopy,piecewise-linear homotopy framework,proximal mappings,generalized equations,normal map,normal cone,generalized equation | Journal | 24 |
Issue | ISSN | Citations |
1 | 0364-765X | 2 |
PageRank | References | Authors |
0.72 | 7 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Stephen C. Billups | 1 | 208 | 40.10 |
| Michael C. Ferris | 2 | 1115 | 142.21 |