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论文类型：期刊论文
发表时间：2008-10-01
发表刊物：NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
收录刊物：SCIE、EI、Scopus
卷号：69
期号：7
页面范围：2095-2113
ISSN号：0362-546X
关键字：augmented Lagrangian; duality; exact penalty representation; tangent cone; normal cone; subderivative; subdifferential
摘要：Tangent cone and (regular) normal cone of a closed set under ail invertible variable transformation around a given point are investigated, which lead to the concepts of theta(-1)-tangent cone of a set and theta(-1)-subderivative of a function. When the notion of theta(-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 -turbation variables. A necessar and sufficient condition for the exact penalty representation under the proposed all-ruented 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 theta(-1)subderivatives. An example of the variable transformation applied to constrained optimization problems is given, which yields several exact penalization results in the literature. (C) 2007 Elsevier Ltd. All rights reserved.