| Title:
|
A note on the uniformity of strong subregularity around the reference point (English) |
| Author:
|
Roubal, Tomáš |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 (print) |
| ISSN:
|
1805-949X (online) |
| Volume:
|
61 |
| Issue:
|
5 |
| Year:
|
2025 |
| Pages:
|
635-646 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This paper investigates strong metric subregularity around the reference point as introduced by H. Gfrerer and J. V. Outrata. In the setting of Banach spaces, we analyse its stability under Lipschitz continuous perturbations and establish its uniformity over compact sets. Our results ensure that the property is preserved under small Lipschitz perturbations, which is crucial for maintaining robustness in variational analysis. Furthermore, we apply the developed theory to parametric inclusion problems. The analysis demonstrates that the uniformity of strong metric subregularity provides a theoretical foundation for addressing stability issues in parametrized optimization and control applications. (English) |
| Keyword:
|
strong metric subregularity |
| Keyword:
|
Lipschitz continuity |
| Keyword:
|
uniformity |
| Keyword:
|
sum stability |
| MSC:
|
49J52 |
| MSC:
|
49J53 |
| MSC:
|
90C33 |
| DOI:
|
10.14736/kyb-2025-5-0635 |
| . |
| Date available:
|
2025-12-19T19:33:02Z |
| Last updated:
|
2025-12-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/153207 |
| . |
| Reference:
|
[1] Adly, S., Cibulka, R., Massias, H.: Variational analysis and generalized equations in electronics..Set-Valued Var. Anal. 21 (2013), 333-358. |
| Reference:
|
[2] Benko, M., Mehlitz, P.: Calmness and calculus: Two basic patterns..Set-Valued Var. Anal. 30 (2021), 81-117. |
| Reference:
|
[3] Cibulka, R., Dontchev, A. L., Kruger, A. Y.: Strong metric subregularity of mappings in variational analysis and optimization..J. Math. Anal. Appl. 457 (2018), 2, 1247-1282. |
| Reference:
|
[4] Cibulka, R., Preininger, J., Roubal, T.: On uniform regularity and strong regularity..Optimization 68 (2019), 2-3, 549-577. |
| Reference:
|
[5] Cibulka, R., Roubal, T.: Solution stability and path-following for a class of generalized equations..In: Control Systems and Mathematical Methods in Economics, vol. 687 of Lecture Notes in Econom. and Math. Systems. Springer, Cham, 2018, pp. 57-80. |
| Reference:
|
[6] Dontchev, A. L., Krastanov, M. I., Rockafellar, R. T., Veliov, V. M.: An {E}uler-{N}ewton continuation method for tracking solution trajectories of parametric variational inequalities..SIAM J. Control Optim. 51 (2013), 3, 1823-1840. |
| Reference:
|
[7] Dontchev, A. L., Rockafellar, R. T.: Implicit Functions and Solution Mappings. A View from Variational Analysis. (Second edition.).Springer, New York 2014. |
| Reference:
|
[8] Gfrerer, H., Outrata, J.: On a semismooth* Newton method for solving generalized equations..SIAM J. Optim. 31 (2021), 1, 489-517. |
| Reference:
|
[9] Gfrerer, H., Outrata, J.: On (local) analysis of multifunctions via subspaces contained in graphs of generalized derivatives..J. Math. Anal. Appl. 508 (2022), 2, 125895. |
| Reference:
|
[10] Ioffe, A. D.: Variational Analysis of Regular Mappings. Theory and Applications..Springer Monographs in Mathematics, Springer, Cham 2017. |
| Reference:
|
[11] Ngai, H. V., Tron, N. H., Théra, M.: Metric regularity of the sum of multifunctions and applications..J. Optim. Theory Appl. 160 (2014), 2, 355-390. |
| Reference:
|
[12] Rockafellar, R. T., Wets, R. J. B.: Variational Analysis, vol. 317 of Grundlehren der Mathematischen Wissenschaften: Fundamental Principles of Mathematical Sciences..Springer-Verlag, Berlin 1998. |
| . |
