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The most well-known technique or method in unconstrained optimization is the conjugate gradient method. It is used to get the greatest solution for the unconstrained optimization problems. This method is used in many fields especially, computer science, and engineering due to its convergence speed, simplicity, and the low memory requirements. A new modified conjugate gradient method is presented in this paper. This method is proved with the strong Wolfe-Powell (SWP) line search that it possesses sufficient descent property, and is globally convergent. Numerical results for a set of 141 test problems show the outperformance of the new proposed formula comparing with other methods using the same line search. The performance of this method is more efficient and better than the others.

The conjugate gradient (CG) and Davidon, Fletcher and Powell (DFP) method are both well known solvers for solving unconstrained optimization problems. In this paper, we proposed a new hybrid DFP-CG method and compared with the ordinary DFP method in terms of number of iteration and CPU times. Numerical results show that the new algorithm is more efficient compared to the ordinary DFP method and proven to posses both sufficient descent and global convergence properties.