Journal of Inequalities and Applications
Volume 2007 (2007), Article ID 19323, 12 pages
doi:10.1155/2007/19323
Research Article
Generalized Augmented Lagrangian Problem and Approximate Optimal Solutions in Nonlinear Programming
Department of Mathematics and Computer Science, Chongqing Normal University, Chongqing 400047, China
Received 19 March 2007; Accepted 29 August 2007
Academic Editor: Yeol Je Cho
Copyright © 2007 Zhe Chen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We introduce some approximate optimal solutions and a generalized augmented Lagrangian in nonlinear programming, establish dual function and dual problem based on the generalized augmented Lagrangian, obtain approximate KKT necessary optimality condition of the generalized augmented Lagrangian dual problem, prove that the approximate stationary points of generalized augmented Lagrangian problem converge to that of the original problem. Our results improve and generalize some known results.