Modified Conjugate Gradient Method with Global Convergence Property

Conjugate gradient method is an efficient method in solving problems with unconstrained optimization , which is especially efficient in dealing large dimension. In light of the conjugate character of conjugate gradient method and the fact that the strength or weakness of an algorithm is more or less determined by the step size and the search direction of the algorithm, a modified conjugate gradient method is proposed in this paper. Some important lemmas and global convergence theorem for the new method are given and proved as follows. The numerical results suggest that the method is convergent and efficient in resolving the given test problems.