Computation of second-order directional stationary points for group sparse optimization

Dingtao Peng, Xiaojun Chen

Research output: Journal article publicationJournal articleAcademic researchpeer-review

1 Citation (Scopus)

Abstract

We consider a nonconvex and nonsmooth group sparse optimization problem where the penalty function is the sum of compositions of a folded concave function and the l2 vector norm for each group variable. We show that under some mild conditions a first-order directional stationary point is a strict local minimizer that fulfils the first-order growth condition, and a second-order directional stationary point is a strong local minimizer that fulfils the second-order growth condition. In order to compute second-order directional stationary points, we construct a twice continuously differentiable smoothing problem and show that any accumulation point of the sequence of second-order stationary points of the smoothing problem is a second-order directional stationary point of the original problem. We give numerical examples to illustrate how to compute a second-order directional stationary point by the smoothing method.

Original languageEnglish
Pages (from-to)348-376
Number of pages29
JournalOptimization Methods and Software
Volume35
Issue number2
DOIs
Publication statusPublished - 3 Mar 2020

Keywords

  • composite folded concave penalty
  • directional stationary point
  • Group sparse optimization
  • nonconvex and nonsmooth optimization
  • smoothing method

ASJC Scopus subject areas

  • Software
  • Control and Optimization
  • Applied Mathematics

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