Author(s)

You-Lin Shang, Sheng-Li Guo, Xiang-Yi Jiang

Department of Mathematics, Henan University of Science and Technology, Luoyang, China.

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.

Nonlinear Programming; NCP Function; Lagrange Function; Multiplier; Convergence

Y. Shang, S. Guo and X. Jiang, "A New Lagrangian Multiplier Method on Constrained Optimization," Applied Mathematics, Vol. 3 No. 10A, 2012, pp. 1409-1414. doi: 10.4236/am.2012.330198.