非凸函数的一类改进BFGS算法的全局收敛性

Global Convergence of a Class of Modified BFGS Algorithm on Nonconvex Functions

文[1]提出了一类改进的BFGS算法,并在目标函数为一致凸的条件下,证明了算法具有全局收敛性。针对该算法,在目标函数为非凸函数时,提出一个假设条件,证明具有wolf线搜索的该算法亦具有全局收敛性。

A class of modified BFGS algorithm is proposed in this paper , and the algorithm is globally covergent under the condition that the objective function is uniformly convex. In this paper,we propose a condition,and show that the class of modified BFGS algorithm with wolf ＇ s line search is also globally convergent under this condition, even when applied to a nonconvex function.