Title :
Error bounds for lower semicontinuous inequality systems
Author :
Wu, Zili ; Ye, Jane J.
Author_Institution :
Dept. of Math. & Stats, Victoria Univ., BC, Canada
Abstract :
Let X be a Banach space and f:X →(-∞, ∞) be a proper and lower semicontinuous function, denoted as S={x ∈ X:f(x)≤0}, ds(x) :=inf{||x-s||:s ∈ S}. We say that the system f(x) ≤ 0 (or s) has a local (global) error bound if S is nonempty and, for some 0 < μ and ε ∈(0,+∞) (ε=+∞), ds(x) ≤ μf(x)+∀x ∈ X with f+(x)<ε, where f(x)+ := max{f(x),0}. We recall the concept of an abstract subdifferential ∂ω subdifferential defined by Wu et al. (2001).
Keywords :
Banach spaces; Hilbert spaces; differentiation; optimisation; Banach space; Hilbert space; error bounds; lower semicontinuous inequality systems; subdifferential; Hilbert space; Sufficient conditions;
Conference_Titel :
Decision and Control, 2002, Proceedings of the 41st IEEE Conference on
Print_ISBN :
0-7803-7516-5
DOI :
10.1109/CDC.2002.1184427