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Meng, Z.Q., Hu, Q.Y. and Dang, C.Y. (2009) A Penalty Function Algorithm with Objective Parameters for Nonlinear Mathematical Programming. Journal of Industrial and Management Optimization, 5, 585-601.
https://doi.org/10.3934/jimo.2009.5.585

has been cited by the following article:

• TITLE: A New Augmented Lagrangian Objective Penalty Function for Constrained Optimization Problems

  AUTHORS: Ying Zheng, Zhiqing Meng

  KEYWORDS: Constrained Optimization Problems, Augmented Lagrangian, Objective Penalty Function, Saddle Point, Algorithm

  JOURNAL NAME: Open Journal of Optimization, Vol.6 No.2, May 19, 2017

  ABSTRACT: In this paper, a new augmented Lagrangian penalty function for constrained optimization problems is studied. The dual properties of the augmented Lagrangian objective penalty function for constrained optimization problems are proved. Under some conditions, the saddle point of the augmented Lagrangian objective penalty function satisfies the first-order Karush-Kuhn-Tucker (KKT) condition. Especially, when the KKT condition holds for convex programming its saddle point exists. Based on the augmented Lagrangian objective penalty function, an algorithm is developed for finding a global solution to an inequality constrained optimization problem and its global convergence is also proved under some conditions.