In the present paper, the problem of estimating the contingent cone to the solution set associated with certain set-valued inclusions is addressed by variational analysis methods and tools. As a main result, inner (resp. outer) approximations, which are expressed in terms of outer (resp. inner) prederivatives of the set-valued term appearing in the inclusion problem, are provided. For the analysis of inner approximations, the evidence arises that the metric increase property for set-valued mappings turns out to play a crucial role. Some of the results obtained in this context are then exploited for formulating necessary optimality conditions for constrained problems, whose feasible region is defined by a set-valued inclusion.

Uderzo, A. (2022). On tangential approximations of the solution set of set-valued inclusions. JOURNAL OF APPLIED ANALYSIS, 28(1), 11-33 [10.1515/jaa-2021-2049].

On tangential approximations of the solution set of set-valued inclusions

Uderzo, A.
2022

Abstract

In the present paper, the problem of estimating the contingent cone to the solution set associated with certain set-valued inclusions is addressed by variational analysis methods and tools. As a main result, inner (resp. outer) approximations, which are expressed in terms of outer (resp. inner) prederivatives of the set-valued term appearing in the inclusion problem, are provided. For the analysis of inner approximations, the evidence arises that the metric increase property for set-valued mappings turns out to play a crucial role. Some of the results obtained in this context are then exploited for formulating necessary optimality conditions for constrained problems, whose feasible region is defined by a set-valued inclusion.
Articolo in rivista - Articolo scientifico
contingent cone; decrease principle; fan; optimality condition; prederivative; Tangential approximation;
English
20-mar-2021
2022
28
1
11
33
open
Uderzo, A. (2022). On tangential approximations of the solution set of set-valued inclusions. JOURNAL OF APPLIED ANALYSIS, 28(1), 11-33 [10.1515/jaa-2021-2049].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/393448
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