无导数线搜索下Broyden-Like方法的全局收敛性

Proof of global convergence of broyden-like method with derivative-free line search

针对文献[1]中提出的无导数线搜索的不足,给出一个新的无导数线搜索,并在此线搜索基础上,研究近似模下降拟牛顿算法所具有的一些性质,并证明了其全局收敛性。

The derivative-free line search in literature[l] has not been well defined. We thus have proposed a new derivative-free line search. Based on this line search, we shew some useful properties of the approximately norm descent quasi-Newton algorithm and reached some conclusions. We then proved the global convergence.