Regularity properties of constrained set-valued mappings

In these notes, we present a general result concerning the Lipschitz regularity of a certain type of set-valued maps often found in constrained optimization and control problems. The class of multifunctions examined in this paper is characterized by means of a set of Lipschitz continuous constraint...

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Bibliographic Details
Published in:Nonlinear analysis 2003-09, Vol.54 (7), p.1337-1353
Main Authors: Papi, Marco, Sbaraglia, Simone
Format: Article
Language:English
Subjects:
Calculus of variations and optimal control
Exact sciences and technology
Generalized Jacobian
Implicit Function Theorem
Lipschitz regularity
Mathematical analysis
Mathematics
Multifunctions
Real functions
Sciences and techniques of general use
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Summary:In these notes, we present a general result concerning the Lipschitz regularity of a certain type of set-valued maps often found in constrained optimization and control problems. The class of multifunctions examined in this paper is characterized by means of a set of Lipschitz continuous constraint functions defined on some Lipschitz manifold. The proof of the regularity result for this class of multifunctions is based on a quantitative version of the Implicit Function Theorem for Lipschitzian maps which provides estimates for the neighborhoods where the implicit map can be defined.
ISSN:0362-546X
1873-5215
DOI:10.1016/S0362-546X(03)00190-1