CG method with modifying βk for solving unconstrained optimization problems

One of the important techniques used for solving the constrained and unconstrained optimization problems is the conjugate gradient CG method, which is one of the efficient techniques used for solving the unconstrained optimization problems due to its advantages of ease of application and its lack of need for large storage capacities as well as its ability at the same time to solve problems that need a high storage capacity (large scale). In this work, this method was modified by combining beta(k) parameters of the Polak-Ribiere (PR) method and beta(k) of the Hestenes-Stiefel (HS) method to solve these kinds of problems. By comparing this method with three famous algorithms, using the Matlab program, the numerical expirement showed that our proposed method is the best.