Metric subregularity for nonclosed convex multifunctions in normed spaces

¹ Department of Mathematics, Yunnan University, Kunming 650091, P. R. China. xyzheng@ynu.edu.cn
² Department of Mathematics, The Chinese University of Hong Kong, Shatin, New Territory, Hong Kong. kfng@math.cuhk.edu.hk

Received: 13 September 2008
Revised: 4 February 2009

Abstract

In terms of the normal cone and the coderivative, we provide some necessary and/or sufficient conditions of metric subregularity for (not necessarily closed) convex multifunctions in normed spaces. As applications, we present some error bound results for (not necessarily lower semicontinuous) convex functions on normed spaces. These results improve and extend some existing error bound results.