We present a new theoretical analysis of local superlinear convergence of classical quasi-Newton methods from the convex Broyden class. As a result, we obtain a significant improvement in the currently known estimates of the convergence rates for these methods. In particular, we show that the corresponding rate of the Broyden–Fletcher–Goldfarb–Shanno method depends only on the product of the dimensionality of the problem and the logarithm of its condition number.

中文翻译：

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经典拟牛顿法超线性收敛的新结果

我们提出了凸Broyden类中经典拟牛顿方法的局部超线性收敛的新理论分析。结果，我们在这些方法的收敛速度的当前已知估计中获得了显着改善。特别是，我们证明了Broyden-Fletcher-Goldfarb-Shanno方法的相应速率仅取决于问题维数与条件数对数的乘积。