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Generalized Augmented Lagrangian Problem and Approximate Optimal Solutions in Nonlinear Programming

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.

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Correspondence to Zhe Chen.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Chen, Z., Zhao, K. & Chen, Y. Generalized Augmented Lagrangian Problem and Approximate Optimal Solutions in Nonlinear Programming. J Inequal Appl 2007, 019323 (2007). https://doi.org/10.1155/2007/19323

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Keywords

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