论文标题
希尔伯特空间中的不确定的牛顿近端方法
Inexact Proximal Newton methods in Hilbert spaces
论文作者
论文摘要
我们考虑使用更新步骤的不精确计算的近端牛顿方法。为此，我们介绍了两个不精确的标准，这些标准表征了这些更新步骤的足够准确性，并在这些方面研究了我们方法的全球收敛和局部加速度。不确定的标准旨在适合我们发现自己所处的希尔伯特太空框架，而在这种情况下，牛顿平滑或有限的维度近端方法的传统不确定标准似乎效率低下。考虑到功能空间中的简单模型问题，该方法的性能及其在有效性上的增益与确切情况相反。
We consider Proximal Newton methods with an inexact computation of update steps. To this end, we introduce two inexactness criteria which characterize sufficient accuracy of these update step and with the aid of these investigate global convergence and local acceleration of our method. The inexactness criteria are designed to be adequate for the Hilbert space framework we find ourselves in while traditional inexactness criteria from smooth Newton or finite dimensional Proximal Newton methods appear to be inefficient in this scenario. The performance of the method and its gain in effectiveness in contrast to the exact case are showcased considering a simple model problem in function space.
