On Error Bound Moduli for Locally Lipschitz and Regular Functions

Minghua Li; Kaiwen Meng; Xiaoqi Yang

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arXiv · 1608.03360

On Error Bound Moduli for Locally Lipschitz and Regular Functions

Minghua Li·Kaiwen Meng·Xiaoqi Yang

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Abstract

In this paper we study local error bound moduli for a locally Lipschitz and regular function via its outer limiting subdifferential set. We show that the distance of 0 from the outer limiting subdifferential of the support function of the subdifferential set, which is essentially the distance of 0 from the end set of the subdifferential set, is an upper estimate of the local error bound modulus. This upper estimate becomes tight for a convex function under some regularity conditions. We show that the distance of 0 from the outer limiting subdifferential set of a lower $\mathcal{C}^1$ function is equal to the local error bound modulus.

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BibTeX RIS

Minghua Li, Kaiwen Meng, Xiaoqi Yang. 2016-08-11. On Error Bound Moduli for Locally Lipschitz and Regular Functions. https://arxiv.org/abs/1608.03360

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