Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/5880
Title: A nonlinear Lagrangian approach to constrained optimization problems
Authors: Yang, XQ 
Huang, XX
Keywords: Augmented Lagrangian
Nonlinear Lagrangian
Zero duality gap
Optimal path
Necessary optimality condition
Smooth approximate variational principle
Issue Date: 2001
Publisher: Society for Industrial and Applied Mathematics
Source: SIAM journal on optimization, 2001, v. 11, no. 4, p. 1119-1144 How to cite?
Journal: SIAM Journal on optimization 
Abstract: In this paper we study nonlinear Lagrangian functions for constrained optimization problems which are, in general, nonlinear with respect to the objective function. We establish an equivalence between two types of zero duality gap properties, which are described using augmented Lagrangian dual functions and nonlinear Lagrangian dual functions, respectively. Furthermore, we show the existence of a path of optimal solutions generated by nonlinear Lagrangian problems and show its convergence toward the optimal set of the original problem. We analyze the convergence of several classes of nonlinear Lagrangian problems in terms of their first and second order necessary optimality conditions.
URI: http://hdl.handle.net/10397/5880
ISSN: 1052-6234
EISSN: 1095-7189
DOI: 10.1137/S1052623400371806
Rights: © 2001 Society for Industrial and Applied Mathematics
Appears in Collections:Journal/Magazine Article

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