一类新的共轭梯度法的全局收敛性(英文)

Global Convergence of a Class of New Conjugate Gradient Methods

本文提出了一类与HS方法相关的新的共轭梯度法.在强Wolfe线搜索的条件下,该方法能够保证搜索方向的充分下降性,并且在不需要假设目标函数为凸的情况下,证明了该方法的全局收敛性.同时,给出了这类新共轭梯度法的一种特殊形式,通过调整参数ρ,验证了它对给定测试函数的有效性.

In this paper, we present a class of new conjugate gradient methods connected with the HS method, which determines the sufficient descent property, and proves the global convergence of such a class of methods with the strong Wolfe line search conditions without assuming the convexity of the objective function. The numerical results show that the new method is efficient for the given test problems. At the same time, a special form of the class of new conjugate gradient methods is given, and verified the efficiency on the test function by adjusting the parameter p.