Modified Preconditioned Conjugate Gradient Algorithms for Lagrange method

This paper is cornered with the improvement of conjugate gradient type methods (CG methods) to solve non-linear constrained optimization problems by using Lagrange method. Most numerical algorithms are sensitive to error due to arithmetic operation , therefore we suggested the self scaling conjugate Gradient method to avoid this difficulty and to increase the ability for solving algorithms for ill- problems. Our new modified CG method shows that , it is too effect when compared with other established algorithms to solve standard constant optimization problems