Ample parameterization of variational inclusions

Citation
Al. Dontchev et Rt. Rockafellar, Ample parameterization of variational inclusions, SIAM J OPTI, 12(1), 2001, pp. 170-187
Citations number
23
Categorie Soggetti
Mathematics
Journal title
SIAM JOURNAL ON OPTIMIZATION
ISSN journal
10526234 → ACNP
Volume
12
Issue
1
Year of publication
2001
Pages
170 - 187
Database
ISI
SICI code
1052-6234(20011023)12:1<170:APOVI>2.0.ZU;2-M
Abstract
For a general category of variational inclusions infinite dimensions, a cla ss of parameterizations, called ample parameterizations, is identified that is rich enough to provide a full theory of Lipschitz-type properties of so lution mappings without the need to resort to the auxiliary introduction of canonical parameters. Ample parameterizations also support a detailed desc ription of the graphical geometry that underlies generalized differentiatio n of solutions mappings. A theorem on proto-derivatives is thereby obtained . The case of a variational inequality over a polyhedral convex set is give n special treatment along with an application to minimizing a parameterized function over such a set.