Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/9356
Title: An augmented Lagrangian approach with a variable transformation in nonlinear programming
Authors: Zhang, L
Yang, X 
Keywords: Augmented Lagrangian
Duality
Exact penalty representation
Normal cone
Subderivative
Subdifferential
Tangent cone
Issue Date: 2008
Publisher: Pergamon Press
Source: Nonlinear analysis : theory, methods and applications, 2008, v. 69, no. 7, p. 2095-2113 How to cite?
Journal: Nonlinear analysis : theory, methods and applications 
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- 1-tangent cone of a set and θ- 1-subderivative of a function. When the notion of θ- 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- 1-subderivatives. An example of the variable transformation applied to constrained optimization problems is given, which yields several exact penalization results in the literature.
URI: http://hdl.handle.net/10397/9356
ISSN: 0362-546X
DOI: 10.1016/j.na.2007.07.048
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