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W. Hua and D. G. Pu, “A Modified QP-Free Feasible Method,” Applied Mathmatical Modelling, Vol. 35, No. 4, 2011, pp. 1696-1708. doi:10.1016/j.apm.2010.10.002

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• 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.