Characterizations of error bounds for lower semicontinuous functions on metric spaces

By Dominique Azé, Jean-Noël Corvellec. 2004

166 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a915416c6b7ddcfd04f499479096dc10c70e9d43

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In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

A survey on error bounds for lower semicontinuous functions (2003, background): “We emphasize the case of a recent characterization of this property which appeared in [5,7].”
Characterizations of Lojasiewicz inequalities and applications (2008, background): “(Strong slope) Let us recall from [18] (see also [28], [6]) the notion of strong slope defined for every x ∈ dom f as follows:”
Characterizations of Lojasiewicz inequalities: Subgradient flows, talweg, convexity (2009, methodology): “…function f is deﬁned by When r 1 = r 2 (respectively r 1 = −∞ ), the above set will be simply denoted by (Strong slope) Let us recall from [18] (see also [28], [6]) the notion of strong slope deﬁned for every x ∈ dom f as follows: where for every a ∈ R we set a where d denotes the distance on X.”
Error Bounds: Necessary and Sufficient Conditions (2010, methodology): “Constant (23) was used for characterizing the error bound property in [2, 4, 43].”
Error bounds and metric subregularity (2014, methodology): “The interested reader is referred to the articles by Azé [1], Azé and Corvellec [2], Corvellec and Motreanu [3], Gfrerer [4], Ioffe [5], Ioffe and Outrata [6], Ngai and Théra [7,8], Jong-Shi Pang [9], Zheng and Ng [10,11] and the references therein.”
Error Bounds and Hölder Metric Subregularity (2014, unknown): “, [2, 4, 13, 22]) with constant τ > 0 at a point x̄ ∈ X with f(x̄) = 0 if there exists a neighbourhood U of x̄ such that τd(x,S(f)) ≤ f+(x) for all x ∈ U.”