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About errors bounds in metric spaces

Authors: Fabian, Marian , Henrion, René , Kruger, Alexander , Outrata, Jiri
Date: 2011
Type: Text , Conference paper
Relation: International Conference Operations Research p. 33-38
Relation: http://purl.org/au-research/grants/arc/DP110102011
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Description: The paper presents a general primal space classification scheme of necessary and suffficient criteria for the error bound property incorporating the existing conditions. Several primal space derivative-like objects - slopes are used to characterize the error bound property of extended-real valued functions on metric sapces.

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Error bounds : Necessary and sufficient conditions

Authors: Fabian, Marian , Henrion, René , Kruger, Alexander , Outrata, Jiri
Date: 2010
Type: Text , Journal article
Relation: Set-Valued and Variational Analysis Vol. 18, no. 2 (2010), p. 121-149
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Description: The paper presents a general classification scheme of necessary and sufficient criteria for the error bound property incorporating the existing conditions. Several derivative-like objects both from the primal as well as from the dual space are used to characterize the error bound property of extended-real-valued functions on a Banach space. Â© 2010 Springer Science+Business Media B.V.

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On semiregularity of mappings

Authors: Cibulka, Radek , Fabian, Marian , Kruger, Alexander
Date: 2019
Type: Text , Journal article
Relation: Journal of Mathematical Analysis and Applications Vol. 473, no. 2 (2019), p. 811-836
Relation: http://purl.org/au-research/grants/arc/DP160100854
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Description: There are two basic ways of weakening the definition of the well-known metric regularity property by fixing one of the points involved in the definition. The first resulting property is called metric subregularity and has attracted a lot of attention during the last decades. On the other hand, the latter property which we call semiregularity can be found under several names and the corresponding results are scattered in the literature. We provide a self-contained material gathering and extending the existing theory on the topic. We demonstrate a clear relationship with other regularity properties, for example, the equivalence with the so-called openness with a linear rate at the reference point is shown. In particular cases, we derive necessary and/or sufficient conditions of both primal and dual type. We illustrate the importance of semiregularity in the convergence analysis of an inexact Newton-type scheme for generalized equations with not necessarily differentiable single-valued part. © 2019 Elsevier Inc.

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