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...

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Published in:SIAM journal on optimization 2016-01, Vol.26 (1), p.448-473
Main Authors: Adly, S., Nacry, F., Thibault, L.
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Language:English
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Mathematics
Optimization and Control
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description 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.
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Optimization and Control
title Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization
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