引入二阶导数的梯度法

Gradiet Method with Introduction of Second Derivative

对最优化方法中的梯度算法进行了改进．当2f/x2=≠0时，将二阶导数与梯度方向相结合，构造出一种新的下降方向d=[1＋δ／（2f／x2）]（f／x），其中δ=1或-1．用新的下降方向设计了一种算法，使梯度法得到改进．新的算法比梯度法的收敛速度快，而且比牛顿法计算量小．

A new descending direction resulted from combining the second derivative with gradient descending direction to improve the calculation of gradient in optimization method is proposed. If 2f/x2≠0, then the new descending direction d= [1+δ/ (2f/x2)] (f/x), where δ= 1or-1. An algorithm is designed with the new descending direction d. The convergence rate of the new method isfaster than that of the gradient method and the amount of computation works is less than that of theNewton method and quasi-Newton method.