Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization

In this paper, we first provide counterexamples showing that sublevels of prox-regular functions and levels of differentiable mappings with Lipschitz derivatives may fail to be prox-regular. Then, we prove the uniform prox-regularity of such sets under usual verifiable qualification conditions. The...

Full description

Saved in:
Bibliographic Details
Published in:SIAM journal on optimization 2016-01, Vol.26 (1), p.448-473
Main Authors: Adly, S., Nacry, F., Thibault, L.
Format: Article
Language:English
Subjects:
Mathematics
Optimization and Control
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper, we first provide counterexamples showing that sublevels of prox-regular functions and levels of differentiable mappings with Lipschitz derivatives may fail to be prox-regular. Then, we prove the uniform prox-regularity of such sets under usual verifiable qualification conditions. The preservation of uniform prox-regularity of intersection and inverse image under usual qualification conditions is also established. Applications to constrained optimization problems are given.
ISSN:1052-6234
1095-7189
DOI:10.1137/15M1032739