Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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PROXIMAL AUGMENTED LAGRANGIAN AND APPROXIMATE OPTIMAL SOLUTIONS IN NONLINEAR PROGRAMMING

  • Chen, Zhe (Department of Mathematics and Computer Science, Chongqing Normal University) ;
  • Huang, Hai Qiao (School of Fashion Art and Engineering, Beijing Institute of Clothing Technology) ;
  • Zhao, Ke Quan (Department of Mathematics and Computer Science, Chongqing Normal University)
  • Published : 2009.01.31
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Abstract

In this paper, we introduce some approximate optimal solutions and an augmented Lagrangian function in nonlinear programming, establish dual function and dual problem based on the augmented Lagrangian function, discuss the relationship between the approximate optimal solutions of augmented Lagrangian problem and that of primal problem, obtain approximate KKT necessary optimality condition of the augmented Lagrangian problem, prove that the approximate stationary points of augmented Lagrangian problem converge to that of the original problem. Our results improve and generalize some known results.

Keywords

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