Abstract
AbstractThis 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.
Funder
Ministerio de Ciencia, Innovación y Universidades
European Regional Development Fund
Generalitat Valenciana
Universidad Miguel Hernández
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Mathematics,Control and Optimization
Reference25 articles.
1. Argáez, C., Cánovas, M.J., Parra, J.: Calmness of linear constraint systems under structured perturbations with an application to the path-following scheme. Set-Valued Var. Anal. 29, 839–860 (2021)
2. Bürgisser, P., Cucker, F.: Condition. The geometry of numerical algorithms, grundlehren der mathematischen wissenschaften fundamental principles of mathematical sciences. Springer, New York (2013)
3. Camacho, J., Cánovas, M. J., Parra, J.: From calmness to Hoffman constants for linear inequality systems, SIAM. J. Optim. 32, 2859–2878 (2022)
4. Cánovas, M.J., Dontchev, A.L., López, M.A., Parra, J.: Metric regularity of semi-infinite constraint systems. Math. Progr. 104B, 329–346 (2005)
5. Cánovas, M.J., Hall, J.A.J., López, M.A., Parra, J.: Calmness of partially perturbed linear systems with an application to the central path. Optimization 68, 465–483 (2019)
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献
1. Preface to Asen L. Dontchev Memorial Special Issue;Computational Optimization and Applications;2023-11-03