BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Xiaoqi Yang (The Hong Kong Polytechnic University) DTSTART:20200812T070000Z DTEND:20200812T080000Z DTSTAMP:20260424T094826Z UID:VAWebinar/8 DESCRIPTION:Title: On error bound moduli for locally Lipschitz and regular functions\nb y Xiaoqi Yang (The Hong Kong Polytechnic University) as part of Variationa l Analysis and Optimisation Webinar\n\n\nAbstract\nWe first introduce for a closed and convex set two classes of subsets: the near and far ends rela tive 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 co nnections between closedness of the far (near) end and the relative contin uity 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 fr om 0 to the end set of the subdifferential set\, is an upper estimate of t he local error bound modulus. This upper estimate becomes tight for a conv ex function under some regularity conditions. We show that the distance fr om 0 to the outer limiting subdifferential set of a lower C^1 function is equal to the local error bound modulus.\n\n\nReferences:\nLi\, M.H.\, Meng K.W. and Yang X.Q.\, On far and near ends of closed and convex sets. Jour nal of Convex Analysis. 27 (2020) 407–421.\nLi\, M.H.\, Meng K.W. and Ya ng X.Q.\, On error bound moduli for locally Lipschitz and regular function s\, Math. Program. 171 (2018) 463–487.\n LOCATION:https://researchseminars.org/talk/VAWebinar/8/ END:VEVENT END:VCALENDAR