An improved Polak–Ribière–Polyak conjugate gradient method with an efficient restart direction

For the large-scale optimization problems, we propose a new conjugate parameter by modifying the denominator of the Polak–Ribiere–Polyak formula, and give its non-negative form. Under the weak Wolfe line search, their corresponding algorithms perform superior to their congener methods, respectively. To guarantee its global convergence, we further introduce a restart condition and a restart direction to improve the proposed method. Under usual assumptions and using the strong Wolfe line search to yielded the step-length, the improved method is sufficient descent and globally convergent. Numerical experiments for the improved method and its comparisons are carried out, and the corresponding numerical results and performance profiles are reported, which showed that the improved method is practicable and efficient for the large-scale optimization problems.