Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/17390
Title: Approximate augmented Lagrangian functions and nonlinear semidefinite programs
Authors: Huang, XX
Teo, KL
Yang, XQ 
Keywords: Semidefinite programming
Augmented Lagrangian
Duality
Exact penalty
Convergence
Stationary point
90C22
90C30
Issue Date: 2006
Publisher: Springer
Source: Acta mathematica Sinica, 2006, v. 22, no. 5, p. 1283-1296 How to cite?
Journal: Acta mathematica Sinica 
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.
URI: http://hdl.handle.net/10397/17390
ISSN: 1439-8516
EISSN: 1439-7617
DOI: 10.1007/s10114-005-0702-6
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