A New Lagrangian Multiplier Method

In this paper, a new augmented Lagrangian function with 4-piecewise linear NCP function is introduce for the solution of nonlinear prgramming problems with equality constrained and ineqality constaianed. It is proved that a solution of the original constrained problem and corresponding values of Lagrange multipliers can be found by solving a uncunstrained minimization of the augmented Lagrange function. Meamwhile, a new Lagrangian multiplier method corresponding with new augmented Lagrangian function is proposed. and this method is implement able and convergent.