An augmented Lagrangian approach with a variable transformation in nonlinear programming

Indexed by:期刊论文

Journal:NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS

Included Journals:SCIE、EI、Scopus

Volume:69

Issue:7

Page Number:2095-2113

ISSN No.: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.

Date of Publication:2008-10-01