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.
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This work is partially supported by the Postdoctoral Fellowship of The Hong Kong Polytechnic University and the Research Grants Council of Hong Kong (PolyU B–Q890)
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Huang, X.X., Teo, K.L. & Yang, X.Q. Approximate Augmented Lagrangian Functions and Nonlinear Semidefinite Programs. Acta Math Sinica 22, 1283–1296 (2006). https://doi.org/10.1007/s10114-005-0702-6
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DOI: https://doi.org/10.1007/s10114-005-0702-6