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.

Classification: 90C31, 90C25, 49J52

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}, publisher = {EDP-Sciences}, volume = {16}, number = {3}, year = {2010}, pages = {601-617}, doi = {10.1051/cocv/2009012}, zbl = {pre05768964}, mrnumber = {2674628}, language = {en}, url = {http://www.numdam.org/item/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://www.numdam.org/item/COCV_2010__16_3_601_0/

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