Existence of augmented Lagrange multipliers for cone constrained optimization problems

Yu Ying Zhou, Jin Chuan Zhou, Xiaoqi Yang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

8 Citations (Scopus)


In this paper, by using an augmented Lagrangian approach, we obtain several sufficient conditions for the existence of augmented Lagrange multipliers of a cone constrained optimization problem in Banach spaces, where the corresponding augmenting function is assumed to have a valley at zero. Furthermore, we deal with the relationship of saddle points, augmented Lagrange multipliers, and zero duality gap property between the cone constrained optimization problem and its augmented Lagrangian dual problem.
Original languageEnglish
Pages (from-to)243-260
Number of pages18
JournalJournal of Global Optimization
Issue number2
Publication statusPublished - 1 Feb 2014


  • Augmented Lagrange multiplier
  • Cone constraints
  • Duality
  • Growth condition

ASJC Scopus subject areas

  • Computer Science Applications
  • Control and Optimization
  • Applied Mathematics
  • Management Science and Operations Research


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