An augmented Lagrangian approach with a variable transformation in nonlinear programming

Indexed by:Journal Article

Date of Publication:2008-10-01

Journal:NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS

Included Journals:Scopus、EI、SCIE

Volume:69

Issue:7

Page Number:2095-2113

ISSN:0362-546X

Key Words:augmented Lagrangian; duality; exact penalty representation; tangent cone; normal cone; subderivative; subdifferential

Abstract: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.