A modified class of conjugate gradient methods with a new nonmonotone Armijo-type line search

Shi and Guo [1] developed a conjugate gradient method with new nonmonotone line search (SG method), their line search is very complex which has two inequalities, and its second inequality is used to generate sufficient descent direction. Here, we modify the SG method by leaving out second inequality. We show that the search direction generated by the modified method at each iteration satisfying the sufficient descent condition. We prove the global convergence of the new method