修正Broyden非凸族在凸组合非单调Wolfe线搜索下收敛的推广分析

Extended Analysis of Convergence for a Modified Broyden's Family under a Convex Combination Non-Monotone Wolfe Line-Search

将一类新提出的凸组合非单调Wolfe线搜索应用到修正Broyden拟牛顿法收敛性分析里.证明了在凸组合非单调Wolfe线搜索下,修正Broyden非凸族具有全局收敛性及超线性收敛性,推广了修正Broyden非凸族收敛分析的线搜索条件.数值结果表明,修正Broyden非凸族在凸组合非单调Wolfe线搜索下的计算效率优于在单调Wolfe搜索下的计算效率.

This paper applies a convex combination non-monotone Wolfe line-search proposed recently to the convergence analysis of Broyden＇s family quasi-Newton method. We show that under the convex combination non-monotone Wolfe line-search, a modified Broyden＇s non-convex family take on global and superlinear convergence. The results extend line-search condition for the convergence analysis of the modified Broyden＇s non-convex family. Finally, primary numerical results are presented. Numerical results show that the computation efficiency of the modified Broyden＇s non-convex family under the convex combination non-monotone Wolfe line-search is superior to that under monotone Wolfe line-search.