Generalized Levitin-polyak well-posedness in constrained optimization

X. X. Huang, Xiaoqi Yang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

111 Citations (Scopus)


In this paper, we consider Levitin-Polyak-type well-posedness for a general constrained optimization problem. We introduce generalized Levitin-Polyak well-posedness and strongly generalized Levitin-Polyak well-posedness. Necessary and sufficient conditions for these types of well-posedness are given. Relations among these types of well-posedness are investigated. Finally, we consider convergence of a class of penalty methods and a class of augmented Lagrangian methods under the assumption of strongly generalized Levitin-Polyak well-posedness.
Original languageEnglish
Pages (from-to)243-258
Number of pages16
JournalSIAM Journal on Optimization
Issue number1
Publication statusPublished - 26 Feb 2007


  • Constrained optimization
  • Generalized Levitin-Polyak well-posedness
  • Generalized minimizing sequence
  • Penalty-type methods

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Software


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