The open covering property, also known in the literature as metric regularity, is investigated for certain classes of set-valued maps in a Banach space setting. The focus of the present study is on a perturbation approach for deriving open covering criteria, which stems from a theorem due to Milyutin, and which is developed here by means of an abstract notion of first-order approximation for single-valued maps between normed spaces. As a result, a criterion is achieved for parametric set-valued maps in terms of open covering of their strict approximation. Two applications are presented: the first one relates to Robinson-type theorems in the context of quasidifferential analysis, whereas the second concerns the estimation of the distance from the solution set to a nonsmooth problem in parametric convex optimization.
Uderzo, A. (2010). On a perturbation approach to open mapping theorems. OPTIMIZATION METHODS & SOFTWARE, 25(1), 143-167 [10.1080/10556780903151524].
Citazione: | Uderzo, A. (2010). On a perturbation approach to open mapping theorems. OPTIMIZATION METHODS & SOFTWARE, 25(1), 143-167 [10.1080/10556780903151524]. | |
Tipo: | Articolo in rivista - Articolo scientifico | |
Carattere della pubblicazione: | Scientifica | |
Presenza di un coautore afferente ad Istituzioni straniere: | No | |
Titolo: | On a perturbation approach to open mapping theorems | |
Autori: | Uderzo, A | |
Autori: | ||
Data di pubblicazione: | 2010 | |
Lingua: | English | |
Rivista: | OPTIMIZATION METHODS & SOFTWARE | |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1080/10556780903151524 | |
Appare nelle tipologie: | 01 - Articolo su rivista |