ESAIM: Control, Optimisation and Calculus of Variations

Table of Contents - July 2010 - Volume 16, Issue 03  

Research Article

Metric subregularity for nonclosed convex multifunctions in normed spaces

Zheng, Xi Yina1 and Ng, Kung Fua2

a1 Department of Mathematics, Yunnan University, Kunming 650091, P. R. China. xyzheng@ynu.edu.cn

a2 Department of Mathematics, The Chinese University of Hong Kong, Shatin, New Territory, Hong Kong. kfng@math.cuhk.edu.hk

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.

(Received September 13 2008)

(Revised February 4 2009)

(Online publication June 18 2009)

Key Words:

  • Metric subregularity;
  • multifunction;
  • normal cone;
  • coderivative

Mathematics Subject Classification:

  • 90C31;
  • 90C25;
  • 49J52