Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/20357
Title: Further study on augmented Lagrangian duality theory
Authors: Huang, XX
Yang, XQ 
Keywords: Augmented Lagrangian
Constraint qualification
Optimality condition
Perturbation function
Zero duality gap
Issue Date: 2005
Publisher: Springer
Source: Journal of global optimization, 2005, v. 31, no. 2, p. 193-210 How to cite?
Journal: Journal of global optimization 
Abstract: In this paper we present a necessary and sufficient condition for a zero duality gap between a primal optimization problem and its generalized augmented Lagrangian dual problems. The condition is mainly expressed in the form of the lower semicontinuity of a perturbation function at the origin. For a constrained optimization problem a general equivalence is established for zero duality gap properties defined by a general nonlinear Lagrangian dual problem and a generalized augmented Lagrangian dual problem respectively. For a constrained optimization problem with both equality and inequality constraints we prove that first-order and second-order necessary optimality conditions of the augmented Lagrangian problems with a convex quadratic augmenting function converge to that of the original constrained program. For a mathematical program with only equality constraints we show that the second-order necessary conditions of general augmented Lagrangian problems with a convex augmenting function converge to that of the original constrained program.
URI: http://hdl.handle.net/10397/20357
ISSN: 0925-5001
EISSN: 1573-2916
DOI: 10.1007/s10898-004-5695-7
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