Regularity Properties of Constrained Set-Valued Mappings
Optimization and Control
2007-05-23 v1 Classical Analysis and ODEs
Abstract
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.
Cite
@article{arxiv.math/0209085,
title = {Regularity Properties of Constrained Set-Valued Mappings},
author = {M. Papi and S. Sbaraglia},
journal= {arXiv preprint arXiv:math/0209085},
year = {2007}
}
Comments
Multifunctions, Lipschitz regularity, Implicit Function Theorem