A complete characterization of the robust isolated calmness of nuclear norm regularized convex optimization problems*

Ying Cui, Defeng Sun

Research output: Journal article publicationJournal articleAcademic researchpeer-review

1 Citation (Scopus)

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.

Original languageEnglish
Pages (from-to)441-458
Number of pages18
JournalJournal of Computational Mathematics
Volume36
Issue number3
DOIs
Publication statusPublished - 28 Mar 2018

Keywords

  • Nuclear norm
  • Robust isolated calmness
  • Second order sufficient condition
  • Strict Robinson constraint qualification

ASJC Scopus subject areas

  • Computational Mathematics

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