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Under either linearity or convexity assumption, several authors have studied the stability of error bounds for inequality systems when the concerned data undergo small perturbations. In this paper, we consider the corresponding issue for a more general conic inequality (most of the constraint systems in optimization can be described by an inequality of this type). In terms of coderivatives for vector-valued functions, we study perturbation analysis of error bounds for conic inequalities in the subsmooth setting. The main results of this paper are new even in the convex/smooth case.
Zheng, Xi Yin 1 ; Ng, Kung-Fu 1
@article{COCV_2019__25__A55_0,
author = {Zheng, Xi Yin and Ng, Kung-Fu},
title = {Stability of error bounds for conic subsmooth inequalities},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
publisher = {EDP-Sciences},
volume = {25},
year = {2019},
doi = {10.1051/cocv/2018047},
zbl = {1439.49029},
mrnumber = {4023128},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2018047/}
}
TY - JOUR AU - Zheng, Xi Yin AU - Ng, Kung-Fu TI - Stability of error bounds for conic subsmooth inequalities JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2019 VL - 25 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/cocv/2018047/ DO - 10.1051/cocv/2018047 LA - en ID - COCV_2019__25__A55_0 ER -
%0 Journal Article %A Zheng, Xi Yin %A Ng, Kung-Fu %T Stability of error bounds for conic subsmooth inequalities %J ESAIM: Control, Optimisation and Calculus of Variations %D 2019 %V 25 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/cocv/2018047/ %R 10.1051/cocv/2018047 %G en %F COCV_2019__25__A55_0
Zheng, Xi Yin; Ng, Kung-Fu. Stability of error bounds for conic subsmooth inequalities. ESAIM: Control, Optimisation and Calculus of Variations, Tome 25 (2019), article no. 55. doi : 10.1051/cocv/2018047. http://geodesic.mathdoc.fr/articles/10.1051/cocv/2018047/
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