Radius theorems for subregularity in infinite dimensions

The paper continues our previous work (Dontchev et al. in Set-Valued Var Anal 28:451–473, 2020) on the radius of subregularity that was initiated by Asen Dontchev. We extend the results of (Dontchev et al. in Set-Valued Var Anal 28:451–473, 2020) to general Banach/Asplund spaces and to other classes...

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Bibliographic Details
Published in:Computational optimization and applications Vol. 86; no. 3; pp. 1117 - 1158
Main Authors: Gfrerer, Helmut, Kruger, Alexander Y.
Format: Journal Article
Language:English
Published: New York Springer US 01.12.2023
Springer Nature B.V
Subjects:
Algorithms
Banach spaces
Computational mathematics
Convex and Discrete Geometry
Management Science
Mathematical functions
Mathematics
Mathematics and Statistics
Operations Research
Operations Research/Decision Theory
Optimization
Perturbation
Robustness (mathematics)
Statistics
Theorems
90C31
Subregularity
49J53
49J52
49K40
Radius theorems
Generalized differentiation
ISSN:0926-6003, 1573-2894
Online Access:Get full text
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Summary:The paper continues our previous work (Dontchev et al. in Set-Valued Var Anal 28:451–473, 2020) on the radius of subregularity that was initiated by Asen Dontchev. We extend the results of (Dontchev et al. in Set-Valued Var Anal 28:451–473, 2020) to general Banach/Asplund spaces and to other classes of perturbations, and sharpen the coderivative tools used in the analysis of the robustness of well-posedness of mathematical problems and related regularity properties of mappings involved in the statements. We also expand the selection of classes of perturbations, for which the formula for the radius of strong subregularity is valid.
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ISSN:0926-6003
1573-2894
DOI:10.1007/s10589-022-00431-6