Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization
本文通过反例说明近正则函数的子水平集和具有Lipschitz导数的可微映射的水平集可能不满足近正则性，然后在通常可验证的约束条件下证明了这些集合的一致近正则性，并应用于约束优化问题。
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.