On Error Bound Moduli for Locally Lipschitz and Regular Functions

2016/08/11 by Li, Minghua, Meng, Kaiwen, Yang, Xiaoqi · 2 citations
#90C30 #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1608.03360

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 C¹ function is equal to the local error bound modulus.

Cited by

• Complexity of Error Bounds for Systems of Linear Inequalities
• Lipschitz upper semicontinuity of linear inequality systems under full perturbations

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