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].

On a perturbation approach to open mapping theorems

UDERZO, AMOS
2010

Abstract

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.
No
Articolo in rivista - Articolo scientifico
Scientifica
Banach constant; Banach lemma; Lyusternik-Graves theorem; Metric regularity; Open covering; Strict -approximation;
English
143
167
Uderzo, A. (2010). On a perturbation approach to open mapping theorems. OPTIMIZATION METHODS & SOFTWARE, 25(1), 143-167 [10.1080/10556780903151524].
Uderzo, A
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10281/8000
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