The radius of metric regularity

By Asen L. Dontchev, A. S. Lewis, R. Tyrrell Rockafellar. 2002

220 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/42a38d7c014195ae7339f8c926256273729dcc1e

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In Biomedical Engineering

In Computational Theory and Mathematics

In Numerical Analysis

Citations in the corpus

Error Bounds, Quadratic Growth, and Linear Convergence of Proximal Methods (2016, background): “establish Theorem 8.6 by appealing to the fundamental relationship between transversality (8.3), metric regularity of constraint systems, and stability of metric regularity under linear perturbations [14]. We begin by recalling the concept of metric regularity – a uniform version of subregularity (D”
Lyusternik-Graves theorem and fixed points (2011, methodology): “It was proven in [10] that if, in addition to the assumptions of Theorem 1, X and Y are finite-dimensional spaces, then the inequality ≥ in (5) becomes equality.”
Characterizations of Lojasiewicz inequalities: Subgradient flows, talweg, convexity (2009, methodology): “This fact is strongly connected to famous classical results in this area (see [23, 45, 32, 49] for example) and in particular to the notion of ρ-metric regularity introduced in [32] by Ioffe.”
ABOUT STATIONARITY AND REGULARITY IN VARIATIONAL ANALYSIS (2009, background): “25 A number of useful regularity properties have been introduced and investigated - see [1, 2, 9, 12, 26 13,20–22,24,28–30,36–40,44–47] and the references therein - the most well recognized and widely 27 used being that of metric regularity.”
METRIC REGULARITY—A SURVEY PART 1. THEORY (2016, background): “1, The concepts of perfect regularity and radius of regularity were introduced, respectively, in [63] and [33].”
Regularity and Conditioning of Solution Mappings in Variational Analysis (2004, methodology): “This definition is slightly weaker than the one we furnished in [ 11 ], where the localization in question was required to be single-valued rather than just nowhere multivalued.”
Characterizations of Lojasiewicz inequalities and applications (2008, background): “This fact is strongly connected to famous classical results in this area (see [19, 35, 28, 39] for example) and in particular to the notion of ρ-metric regularity introduced in [28] by A.”
Randomized Methods for Linear Constraints: Convergence Rates and Conditioning (2008, unknown): “[13]) modulus of regularity of 1 at x̄ for b̄= 1 rad1 x̄ b̄ (15)”
Strong metric subregularity of mappings in variational analysis and optimization (2017, result): “A far reaching generalization of this result was proved in [16], see also [15, Theorem 6A.”