In this paper, a modified conjugate gradient method is presented for solving large-scale unconstrained optimization problems, which possesses the sufficient descent property with Strong Wolfe-Powell line search. A global convergence result was proved when the (SWP) line search was used under some conditions. Computational results for a set consisting of 138 unconstrained optimization test problems showed that this new conjugate gradient algorithm seems to converge more stable and is superior to other similar methods in many situations.

In this paper, we suggest a new nonlinear conjugate gradient method for solving large scale unconstrained optimization problems. We prove that the new conjugate gradient coefficient k β with exact line search is globally convergent. Preliminary numerical results with a set of 116 unconstrained optimization problems show that k β is very promising and efficient when compared to the other conjugate gradient coefficients Fletcher-Reeves) (FR and Polak-Ribiere-Polyak) (PRP .

In this paper, we compared the performance profile of the classical conjugate gradient coefficients FR , PRP with two new k .These two new k possess global convergence properties using the exact line search. Preliminary numerical results show that, the two new k is very promising and efficient when compared to CG coefficients FR , PRP .

In this paper, an efficient nonlinear modified PRP conjugate gradient method is presented for solving large-scale unconstrained optimization problems. The sufficient descent property is satisfied under strong Wolfe-Powell (SWP) line search by restricting the parameter 4 / 1  . The global convergence result is established under the (SWP) line search conditions. Numerical results, for a set consisting of 133 unconstrained optimization test problems, show that this method is better than the PRP method and the FR method.

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