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Journal Articles SIAM Journal on Optimization Year : 2016

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

Abstract

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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Dates and versions

hal-01313215 , version 1 (29-11-2019)

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Samir Adly, Florent Nacry, Lionel Thibault. Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization, 2016, 26 (1), pp.448-473. ⟨10.1137/15M1032739⟩. ⟨hal-01313215⟩
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