扰动谱尺度BFGS算法及收敛性分析

Spectral Analysis of Fluctuation Scale BFGS Algorithm and Its Convergence

在前人提出的扰动BFGS算法的基础上,结合谱尺度算法的思想,提出一种扰动谱尺度BFGS算法,建立算法的全局收敛性定理,本研究证明该扰动谱尺度BFGS算法在一定条件下采用单调Wolfe-Powell型线性搜索和非单调Wolfe-Powell型线性搜索均具有全局收敛性,同时还证明采用单调Wolfe-Powell型线性搜索具有R-线性收敛性.

The predecessors presented disturbance based on BFGS algorithm, combined with the spectral scaling algorithm, a perturbation spectrum scale BFGS algorithm is proposed, the global convergence theorem is established, a perturbation spectrum scale BFGS algorithm is proposed, this study proves that the algorithm using monotone Wolfe-Powell type line search and nonmonotone Wolfe-Powell type line search in certain conditions have global convergence; the paper also proves that the algorithm using monotone Wolfe-Powell type line search with R - linear convergence.