带调整线搜索方向的变尺度算法

Variable Metric Algorithms with Revised Search Direction

为了确保变尺度算法在"坏条件"下的收敛性,本文提出对原算法的线搜索方向作适当地调益的方法,并且证明了带调整线搜索方向的 Broyden 类算法,无论线搜索是否精确,它对连续可微函数是收敛的,对一致凸函数是 Q-超线性收敛的.

In order to guarantee the convergence of the variable metric algorithms in bad case,we give a class of Broyden Algorithms with revised search direction. We prove that these algorithms are globally convergent for the continuous differentiable function and the rate of convergence is Q-superlinear for the uniformly convex objective function.