Author(s)

Ying Zheng¹, Zhiqing Meng²

¹Department of Basic Courses, College of Basic Science, Ningbo Dahongying University, Ningbo, China.
²College of Economics and Management, Zhejiang University of Technology, Hangzhou, China.

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.

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

Zheng, Y. and Meng, Z. (2017) A New Augmented Lagrangian Objective Penalty Function for Constrained Optimization Problems. Open Journal of Optimization, 6, 39-46. doi: 10.4236/ojop.2017.62004.