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.

Keywords: metric subregularity, multifunction, normal cone, coderivative

@article{COCV_2010__16_3_601_0, author = {Zheng, Xi Yin and Ng, Kung Fu}, title = {Metric subregularity for nonclosed convex multifunctions in normed spaces}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {601--617}, publisher = {EDP-Sciences}, volume = {16}, number = {3}, year = {2010}, doi = {10.1051/cocv/2009012}, mrnumber = {2674628}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv/2009012/} }

TY - JOUR AU - Zheng, Xi Yin AU - Ng, Kung Fu TI - Metric subregularity for nonclosed convex multifunctions in normed spaces JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2010 SP - 601 EP - 617 VL - 16 IS - 3 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2009012/ DO - 10.1051/cocv/2009012 LA - en ID - COCV_2010__16_3_601_0 ER -

%0 Journal Article %A Zheng, Xi Yin %A Ng, Kung Fu %T Metric subregularity for nonclosed convex multifunctions in normed spaces %J ESAIM: Control, Optimisation and Calculus of Variations %D 2010 %P 601-617 %V 16 %N 3 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2009012/ %R 10.1051/cocv/2009012 %G en %F COCV_2010__16_3_601_0

Zheng, Xi Yin; Ng, Kung Fu. Metric subregularity for nonclosed convex multifunctions in normed spaces. ESAIM: Control, Optimisation and Calculus of Variations, Volume 16 (2010) no. 3, pp. 601-617. doi : 10.1051/cocv/2009012. http://archive.numdam.org/articles/10.1051/cocv/2009012/

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