For the large-scale optimization problems, we propose a new conjugate parameter by modifying the denominator of the Polak–Ribière–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.

对于大规模优化问题，我们通过修改Polak-Ribière-Polyak公式的分母，提出一个新的共轭参数，并给出其非负形式。在弱沃尔夫线搜索下，它们相应的算法分别优于同类方法。为了保证其全局收敛，我们进一步引入了重启条件和重启方向来改进所提出的方法。在通常的假设和使用强沃尔夫线搜索产生步长的情况下，改进的方法是充分下降和全局收敛的。进行了改进方法的数值实验及其比较，并报告了相应的数值结果和性能曲线，