一类新型的杂交共轭梯度法

A New Type of Hybrid Conjugate Gradient Methods

提出了一个共轭梯度法βk的新公式并讨论了其性质,然后基于新参数公式,给出了一类新型的杂交共轭梯度法,该方法无需线搜索仍具有充分下降性,在弱Wolfe-Powell线搜索下具有全局收敛性.通过数值试验对新方法与HZ方法和PRP方法进行比较,结果表明新方法更有效.

The paper puts forward a new conjugate gradient method βk and discusses its properties. Then,based on a new formula,the author proposes a new type of hybrid conjugate gradient method,which retains a sufficiently descent direction without utilizing the line search. Under the weak Wolfe-Powell line search,the method proves to be globally convergent. Numerical results show that the new method performs much better than both HZ and PRP methods.