Approximate augmented lagrangian functions and nonlinear semidefinite programs

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

Research output: Journal article publicationJournal articleAcademic researchpeer-review

13 Citations (Scopus)

Abstract

In this paper, an approximate augmented Lagrangian function for nonlinear semidefinite programs is introduced. Some basic properties of the approximate augmented Lagrange function such as monotonicity and convexity are discussed. Necessary and sufficient conditions for approximate strong duality results are derived. Conditions for an approximate exact penalty representation in the framework of augmented Lagrangian are given. Under certain conditions, it is shown that any limit point of a sequence of stationary points of approximate augmented Lagrangian problems is a KKT point of the original semidefinite program and that a sequence of optimal solutions to augmented Lagrangian problems converges to a solution of the original semidefinite program.
Original languageEnglish
Pages (from-to)1283-1296
Number of pages14
JournalActa Mathematica Sinica, English Series
Volume22
Issue number5
DOIs
Publication statusPublished - 1 Sep 2006

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this