基于修正割线方程的BB梯度法

BB Gradient Method Based on Modified Secant Equation

将修正的割线方程和BB梯度法结合起来,从而得到一类修正的BB步长,再利用Zhang-Hager非单调线搜索,提出一个改进的BB梯度方法(MB法)。在一定的假设下,MB法是具有全局收敛性的。同时对MB法和同类型的几个BB方法进行大量的数值试验,结果表明MB法的数值效果是最好的。

A modified BB gradient method(MB method)is proposed by combining the modified secant equation with the BB gradient method,thus obtaining a class of modified BB steps,and then using ZhangHager nonmonotonic line search.Under certain assumptions,the MB method is globally convergent.A large number of numerical experiments are also conducted on the MB method and several BB methods of the same type,and the results show that the MB method is the best numerically.