Title of article :
An augmented Lagrangian approach with a variable transformation in nonlinear programming Original Research Article
Author/Authors :
Liwei Zhang، نويسنده , , Xiaoqi Yang، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2008
Pages :
19
From page :
2095
To page :
2113
Abstract :
Tangent cone and (regular) normal cone of a closed set under an invertible variable transformation around a given point are investigated, which lead to the concepts of θ−1θ−1-tangent cone of a set and θ−1θ−1-subderivative of a function. When the notion of θ−1θ−1-subderivative is applied to perturbation functions, a class of augmented Lagrangians involving an invertible mapping of perturbation variables are obtained, in which dualizing parameterization and augmenting functions are not necessarily convex in perturbation variables. A necessary and sufficient condition for the exact penalty representation under the proposed augmented Lagrangian scheme is obtained. For an augmenting function with an Euclidean norm, a sufficient condition (resp., a sufficient and necessary condition) for an arbitrary vector (resp., 0) to support an exact penalty representation is given in terms of θ−1θ−1-subderivatives. An example of the variable transformation applied to constrained optimization problems is given, which yields several exact penalization results in the literature.
Keywords :
subdifferential , Subderivative , Augmented Lagrangian , Duality , Exact penalty representation , Tangent cone , Normal cone
Journal title :
Nonlinear Analysis Theory, Methods & Applications
Serial Year :
2008
Journal title :
Nonlinear Analysis Theory, Methods & Applications
Record number :
860503
Link To Document :
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