不精确线搜索条件下锥模型Broyden凸族算法的收敛速率

Convergence Rate of Conic Broyden Convex Family Under Imperfect Line Search

在一定假设条件下的锥模型Broyden凸族算法的局部收敛性和全局收敛性已有人研究过。本文中进一步研究不精确线搜索条件下锥模型Broyden凸族算法的收敛速率。证明了如果初值x1充分接近强局部极小点x*,那么族中任一算法所产生的点列都是R-局部收敛的，且其R-收敛阶至少是τ≥2，而不需要假设A1充分靠近海色阵2f(x*）。

After the study on local and global convergence of conic Broyden convex family under certain conditions, the convergence rate of it under the imperfect line search is extended. It is proved that all the members in the family are convergent locally with R-order τ≥2 at least without the hypothesis of A, close to 2f(x. ) if the starting point x1 is close to x* enough.