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Journal of Inequalities and Applications
Journal of Inequalities and Applications Cover Image
  • Research Article
  • Open Access

Generalized Augmented Lagrangian Problem and Approximate Optimal Solutions in Nonlinear Programming

Journal of Inequalities and Applications20072007:019323

https://doi.org/10.1155/2007/19323

©  Zhe Chen et al. 2007

  • Received: 19 March 2007
  • Accepted: 29 August 2007
  • Published:

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.

Keywords

  • Optimality Condition
  • Stationary Point
  • Original Problem
  • Dual Problem
  • Dual Function

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Authors’ Affiliations

(1)
Department of Mathematics and Computer Science, Chongqing Normal University, Chongqing, 400047, China

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Copyright

© Zhe Chen et al. 2007

This article is published under license to BioMed Central Ltd. 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.

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