Regularized Newton methods for convex minimization problems with singular solutions

Dong Hui Li, Masao Fukushima, Liqun Qi, Nobuo Yamashita

Research output: Journal article publicationJournal articleAcademic researchpeer-review

34 Citations (Scopus)

Abstract

This paper studies convergence properties of regularized Newton methods for minimizing a convex function whose Hessian matrix may be singular everywhere. We show that if the objective function is LC2, then the methods possess local quadratic convergence under a local error bound condition without the requirement of isolated nonsingular solutions. By using a backtracking line search, we globalize an inexact regularized Newton melhod. We show that the unit stepsize is accepted eventually. Limited numerical experiments are presented, which show the practical advantage of the method.
Original languageEnglish
Pages (from-to)131-147
Number of pages17
JournalComputational Optimization and Applications
Volume28
Issue number2
DOIs
Publication statusPublished - 1 Jul 2004

Keywords

  • Global convergence
  • Minimization problem
  • Quadratic convergence
  • Regularized newton methods
  • Unit step

ASJC Scopus subject areas

  • Applied Mathematics
  • Control and Optimization
  • Management Science and Operations Research
  • Computational Mathematics

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