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A New Lagrangian Multiplier Method on Constrained Optimization

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DOI: 10.4236/am.2012.330198    4,697 Downloads   7,745 Views  


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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

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.


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