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Approximate Augmented Lagrangian Functions and Nonlinear Semidefinite Programs 被引量:3

Approximate Augmented Lagrangian Functions and Nonlinear Semidefinite Programs
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摘要 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. 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.
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2006年第5期1283-1296,共14页 数学学报(英文版)
基金 This work is partially supported by the Postdoctoral Fellowship of The Hong Kong Polytechnic University the Research Grants Council of Hong Kong(PolyU B-Q890)
关键词 semidefinite programming augmented Lagrangian DUALITY exact penalty convergence stationary point semidefinite programming, augmented Lagrangian, duality, exact penalty, convergence,stationary point
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