论文标题
贪婪的准Newton方法，具有明确的超级线性收敛
Greedy Quasi-Newton Methods with Explicit Superlinear Convergence
论文作者
论文摘要
在本文中，我们研究了准Newton方法的贪婪变体。它们基于Broyden家族的某个子类的更新公式。特别是，该子类包括知名的DFP，BFG和SR1更新。但是，与经典的准牛顿方法相反，该方法使用连续迭代的差异来更新Hessian近似值，我们的方法应用了基本向量，贪婪地选择了以最大程度地提高进度的一定程度。对于贪婪的准Newton方法，我们根据其局部超线性收敛的速率建立了一个明确的非质子束缚，其中包含收缩因子，具体取决于迭代计数器的平方。我们还表明，这些方法产生了黑森州近似值，其偏离精确的黑森线性收敛到零。
In this paper, we study greedy variants of quasi-Newton methods. They are based on the updating formulas from a certain subclass of the Broyden family. In particular, this subclass includes the well-known DFP, BFGS and SR1 updates. However, in contrast to the classical quasi-Newton methods, which use the difference of successive iterates for updating the Hessian approximations, our methods apply basis vectors, greedily selected so as to maximize a certain measure of progress. For greedy quasi-Newton methods, we establish an explicit non-asymptotic bound on their rate of local superlinear convergence, which contains a contraction factor, depending on the square of the iteration counter. We also show that these methods produce Hessian approximations whose deviation from the exact Hessians linearly convergences to zero.
