A Polak–Ribière–Polyak (PRP) algorithm is one of the oldest and popular conjugate gradient algorithms for solving nonlinear unconstrained optimization problems. In this paper, we present a q-variant of the PRP (q-PRP) method for which both the sufficient and conjugacy conditions are satisfied at every iteration. The proposed method is convergent globally with standard Wolfe conditions and strong Wolfe conditions. The numerical results show that the proposed method is promising for a set of given test problems with different starting points. Moreover, the method reduces to the classical PRP method as the parameter q approaches 1.

中文翻译：

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甲q -Polak-Ribière-Polyak共轭梯度算法为无约束优化问题

Polak–Ribière–Polyak（PRP）算法是用于解决非线性无约束优化问题的最古老且流行的共轭梯度算法之一。在本文中，我们提出了PRP（q-PRP）方法的q变量，对于该变量，每次迭代都满足充分条件和共轭条件。所提出的方法在标准Wolfe条件和强Wolfe条件下全局收敛。数值结果表明，所提出的方法对于具有不同起点的一组给定测试问题很有希望。此外，随着参数q接近1，该方法简化为经典PRP方法。