The rate of convergence of the augmented Lagrangian method for nonlinear semidefinite programming

Defeng Sun, J. Sun, L. Zhang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

88 Citations (Scopus)


We analyze the rate of local convergence of the augmented Lagrangian method in nonlinear semidefinite optimization. The presence of the positive semidefinite cone constraint requires extensive tools such as the singular value decomposition of matrices, an implicit function theorem for semismooth functions, and variational analysis on the projection operator in the symmetric matrix space. Without requiring strict complementarity, we prove that, under the constraint nondegeneracy condition and the strong second order sufficient condition, the rate of convergence is linear and the ratio constant is proportional to 1/c, where c is the penalty parameter that exceeds a threshold c? > 0 . © 2007 Springer-Verlag.
Original languageEnglish
Pages (from-to)349-391
Number of pages43
JournalMathematical Programming
Issue number2
Publication statusPublished - 1 Aug 2008
Externally publishedYes


  • Nonlinear semidefinite programming
  • Rate of convergence
  • The augmented Lagrangian method
  • Variational analysis

ASJC Scopus subject areas

  • Software
  • Mathematics(all)

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