A comprehensive characterization of the robust isolated calmness of Ky Fan $ k $-norm regularized convex matrix optimization problems
This paper extends a result of isolated calmness for nuclear norm regularized convex optimization problems to Ky Fan $ k $-norm regularized convex optimization problems. We find that there exists a certain equivalence relationship among the critical cones of the Ky Fan $ k $-norm function and its co...
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2025-03-01
|
| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2025227 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | This paper extends a result of isolated calmness for nuclear norm regularized convex optimization problems to Ky Fan $ k $-norm regularized convex optimization problems. We find that there exists a certain equivalence relationship among the critical cones of the Ky Fan $ k $-norm function and its conjugate as well as the 'sigma term', namely, the conjugate function of the parabolic second-order directional derivative of the Ky Fan $ k $-norm. By establishing the equivalence between the primal (dual) strict Robinson constraint qualification (SRCQ) and the dual (primal) second-order sufficient condition (SOSC), we derive a series of complete characterizations of the robust isolated calmness of the Karush-Kuhn-Tucker (KKT) mapping for Ky Fan $ k $-norm regularized convex matrix optimization problems. The obtained results enrich the stability theory of the Ky Fan $ k $-norm regularized convex optimization problems and further enhance the usability of the related algorithms. |
|---|---|
| ISSN: | 2473-6988 |