Augmented lagrangian and nonlinear semidefinite programs

X.X. Huang, Xiaoqi Yang, K.L. Teo

Research output: Chapter in book / Conference proceedingChapter in an edited book (as author)Academic research

Abstract

In this paper, we introduce an augmented Lagrangian for nonlinear semidefinite programs. Some basic properties of the augmented Lagrangian such as differentiabilty, monotonicity and convexity, are discussed. Necessary and sufficient conditions for a strong duality property and an exact penalty representation in the framework of augmented Lagrangian are derived. Under certain conditions, it is shown that any limit point of a sequence of stationary points of augmented Lagrangian problems is a Karuh, Kuhn-Tucker (for short, KKT) point of the original semidefinite program.
Original languageEnglish
Title of host publicationVariational analysis and applications
PublisherSpringer
Pages513-529
Number of pages17
ISBN (Electronic)9780387242767
ISBN (Print)9780387242095
DOIs
Publication statusPublished - 2005

Keywords

  • Semidefinite programming
  • Augmented Lagrangian
  • Duality
  • Exact penalization
  • Convergence
  • Stationary point

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