基于混合割线方程修正的BB梯度法

A Modified BB Gradient Method Based on Hybrid Secant Equation

在Barzilai-Borwein(BB)梯度法的基础上对步长的选择做出了一个新的改进,该步长公式是基于混合割线方程提出的,不仅利用了更多迭代点处的函数值和梯度值信息,而且其对应的算法能进一步改进一类经典的BB型方法.在基本假设下,该方法具有全局收敛性.数值结果表明,所改进的方法数值性能要优于这一类BB型方法.

Based on the Barzilai-Borwein(BB)gradient method,a new improvement was made on the selection of stepsize.The stepsize formula was proposed based on the hybrid secant equation.It not only made use of the function value and gradient value information at more iteration points,but also its corresponding algorithm could further improve a class of classical BB-like methods.Under mild assumptions,the method has global convergence.Numerical results showed that the numerical performance of the improved method was better than those classical BB-like methods.