Robust and continuous metric subregularity for linear inequality systems

This paper introduces two new variational properties, robust and continuous metric subregularity, for finite linear inequality systems under data perturbations. The motivation of this study goes back to the seminal work by Dontchev, Lewis, and Rockafellar (2003) on the radius of metric regularity. I...

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Bibliographic Details
Published in:	Computational optimization and applications Vol. 86; no. 3; pp. 967 - 988
Main Authors:	Camacho, J., Cánovas, M. J., López, M. A., Parra, J.
Format:	Journal Article
Language:	English
Published:	New York Springer US 01-12-2023 Springer Nature B.V
Subjects:	Algorithms Convex and Discrete Geometry Linear functions Linear programming Management Science Mathematics Mathematics and Statistics Operations Research Operations Research/Decision Theory Optimization Perturbation Regularity Robustness Statistics 90C31 Feasible set mapping Radius of metric subregularity 49J53 15A39 90C05 Linear inequality systems Calmness
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Summary:	This paper introduces two new variational properties, robust and continuous metric subregularity, for finite linear inequality systems under data perturbations. The motivation of this study goes back to the seminal work by Dontchev, Lewis, and Rockafellar (2003) on the radius of metric regularity. In contrast to the metric regularity, the unstable continuity behavoir of the (always finite) metric subregularity modulus leads us to consider the aforementioned properties. After characterizing both of them, the radius of robust metric subregularity is computed and some insights on the radius of continuous metric subregularity are provided.
ISSN:	0926-6003 1573-2894
DOI:	10.1007/s10589-022-00437-0