Publication ahead of print Issue ESAIM: COCV DOI 10.1051/cocv/2009012 Published online 18 June 2009

ESAIM: COCV
DOI: 10.1051/cocv/2009012

Metric subregularity for nonclosed convex multifunctions in normed spaces

Xi Yin Zheng¹ and Kung Fu Ng<sup>2

1</sup>  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 September 13, 2008. Revised February 4, 2009. Published online June 18, 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.

Mathematics Subject Classification. 90C31, 90C25, 49J52

Key words: Metric subregularity, multifunction, normal cone, coderivative


© EDP Sciences, SMAI 2009

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