TITLE:
A New Lagrangian Multiplier Method on Constrained Optimization
AUTHORS:
You-Lin Shang, Sheng-Li Guo, Xiang-Yi Jiang
KEYWORDS:
Nonlinear Programming; NCP Function; Lagrange Function; Multiplier; Convergence
JOURNAL NAME:
Applied Mathematics,
Vol.3 No.10A,
November
1,
2012
ABSTRACT: In this paper, a new augmented Lagrangian function with 4-piecewise linear NCP function is introduced for solving nonlinear programming problems with equality constrained and inequality constrained. It is proved that a solution of the original constrained problem and corresponding values of Lagrange multipliers can be found by solving an unconstrained minimization of the augmented Lagrange function. Meanwhile, a new Lagrangian multiplier method corresponding with new augmented Lagrangian function is proposed. And this method is implementable and convergent.