A Complete Characterization of the Robust Isolated Calmness of Nuclear Norm Regularized Convex Optimization Problems
Year: 2018
Author: Ying Cui, Defeng Sun
Journal of Computational Mathematics, Vol. 36 (2018), Iss. 3 : pp. 441–458
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1709-m2017-0034
Journal of Computational Mathematics, Vol. 36 (2018), Iss. 3 : pp. 441–458
Published online: 2018-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: Robust isolated calmness Nuclear norm Second order sufficient condition Strict Robinson constraint qualification.