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

Zhe Chen, Kequan Zhao, and Yuke Chen

 Department of Mathematics and Computer Science, Chongqing Normal University, Chongqing 400047, China
Received 19 March 2007; Accepted 29 August 2007

Recommended by Yeol Je Cho

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.