Title:  On error bound moduli for locally Lipschitz and regular functions

Speaker: Xiaoqi Yang (Hong Kong PolyU)

Date and Time: August 12th, 2020, 17:00 AEST (Register here for remote connection via Zoom)

Abstract: We first introduce for a closed and convex set two classes of subsets: the near and far ends relative to a point, and give some full characterizations for these end sets by virtue of the face theory of closed and convex sets. We provide some connections between closedness of the far (near) end and the relative continuity of the gauge (cogauge) for closed and convex sets. We illustrate that the distance from 0 to the outer limiting subdifferential of the support function of the subdifferential set, which is essentially the distance from 0 to 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 from 0 to the outer limiting subdifferential set of a lower C^1 function is equal to the local error bound modulus.

References:
Li, M.H., Meng K.W. and Yang X.Q., On far and near ends of closed and convex sets. Journal of Convex Analysis. 27 (2020) 407–421.
Li, M.H., Meng K.W. and Yang X.Q., On error bound moduli for locally Lipschitz and regular functions, Math. Program. 171 (2018) 463–487.