@article{Yin2025, 
author = {Ziran Yin and Chongyang Liu and Xiaoyu Chen and Jihong Zhang and Jinlong Yuan},
title = {A comprehensive characterization of the robust isolated calmness of Ky Fan    k-norm regularized convex matrix optimization problems},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {3},
pages = {4955-4969},
keywords = {isolated calmness, Ky Fan k-norm, critical cone, second-order sufficient condition, strict Robinson constraint qualification},
url = {https://www.sciopen.com/article/10.3934/math.2025227},
doi = {10.3934/math.2025227},
abstract = {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.}
}