Regularity Properties of Constrained Set-Valued Mappings

Details Regularity Properties of Constrained Set-Valued Mappings Regularity Properties of Constrained Set-Valued Mappings

2002-09-09

arxiv.org/abs/math/0209085v1

Mathematics

Optimization and Control

Multifunctions, Lipschitz regularity, Implicit Function Theorem

Scientific paper

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.

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