Use NCP Function For Solving The KKT System Of Inequality-Constrained Optimization Problems

This paper choose NCP functionφ(a ,b) = |a - b|~3 - a~3 - b~3 which was presented by Mangasarian,this function is smooth about a and b.We use this NCP function to take the KKT system of Inequality-Constrained Problems into smooth equations ,because these equations are smooth,so it is convenient when we are solving these equations.On the base of the advantages of some methods in this paper,we use Newton-SVD method to solve medium or small problems F ( z ) = 0,and use line search Newton-CG method to solve large problems F ( z ) = 0 which are smooth and nonlinear.This paper is organized as follows.In chapter 1,the background and main results of this paper are given.We introduce the NCP function in chapter 2.We study and research to use NCP function for solving the KKT system of Inequality-Constrained Problems in chapter 3.In chapter 4,we preset two algorithms and analyze their convergence.In chapter 5,we give the results of the experiments.At last,we present the examples in the appendix.