TY  - JOUR
AU  - Yin, Ziran
AU  - Liu, Chongyang
AU  - Chen, Xiaoyu
AU  - Zhang, Jihong
AU  - Yuan, Jinlong
PY  - 2025
TI  - A comprehensive characterization of the robust isolated calmness of Ky Fan    k-norm regularized convex matrix optimization problems
JO  - AIMS Mathematics
SP  - 4955
EP  - 4969
VL  - 10
IS  - 3
AB  - 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.
UR  - https://doi.org/10.3934/math.2025227
DO  - 10.3934/math.2025227