TY - JOUR
T1 - A Complete Characterization of the Robust Isolated Calmness of Nuclear Norm Regularized Convex Optimization Problems
AU - Cui , Ying
AU - Sun , Defeng
JO - Journal of Computational Mathematics
VL - 3
SP - 441
EP - 458
PY - 2018
DA - 2018/06
SN - 36
DO - http://doi.org/10.4208/jcm.1709-m2017-0034
UR - https://global-sci.org/intro/article_detail/jcm/12270.html
KW - Robust isolated calmness, Nuclear norm, Second order sufficient condition, Strict Robinson constraint qualification.
AB - <p style="text-align: justify;">In this paper, we provide a complete characterization of the robust isolated calmness
of the Karush-Kuhn-Tucker (KKT) solution mapping for convex constrained optimization
problems regularized by the nuclear norm function. This study is motivated by the recent
work in [8], where the authors show that under the Robinson constraint qualification at a
local optimal solution, the KKT solution mapping for a wide class of conic programming
problems is robustly isolated calm if and only if both the second order sufficient condition
(SOSC) and the strict Robinson constraint qualification (SRCQ) are satisfied. Based on
the variational properties of the nuclear norm function and its conjugate, we establish
the equivalence between the primal/dual SOSC and the dual/primal SRCQ. The derived
results lead to several equivalent characterizations of the robust isolated calmness of the
KKT solution mapping and add insights to the existing literature on the stability of nuclear
norm regularized convex optimization problems.</p>