Optimality conditions and a smoothing trust region newton method for nonlipschitz optimization

Xiaojun Chen, Lingfeng Niu, Yaxiang Yuan

Research output: Journal article publicationJournal articleAcademic researchpeer-review

68 Citations (Scopus)


Regularized minimization problems with nonconvex, nonsmooth, perhaps non- Lipschitz penalty functions have attracted considerable attention in recent years, owing to their wide applications in image restoration, signal reconstruction, and variable selection. In this paper, we derive affine-scaled second order necessary and sufficient conditions for local minimizers of such minimization problems. Moreover, we propose a global convergent smoothing trust region Newton method which can find a point satisfying the affine-scaled second order necessary optimality condition from any starting point. Numerical examples are given to demonstrate the effectiveness of the smoothing trust region Newton method.
Original languageEnglish
Pages (from-to)1528-1552
Number of pages25
JournalSIAM Journal on Optimization
Issue number3
Publication statusPublished - 29 Oct 2013


  • Convergence
  • Non-Lipschitz
  • Nonsmooth nonconvex optimization
  • Penalty function
  • Regularized optimization
  • Smoothing methods
  • Trust region Newton method

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Software


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