论文标题
增强牛顿优化方法：全球线性速率和动量解释
Augmented Newton Method for Optimization: Global Linear Rate and Momentum Interpretation
论文作者
论文摘要
我们提出了牛顿方法的两种变体，以解决无约束的最小化问题。我们的方法利用优化技术，例如惩罚和增强拉格朗日方法来生成牛顿方法的新型变体，即newton方法和增强的牛顿方法。在此过程中，我们恢复了一些著名的现有牛顿方法变体，例如抑制牛顿，莱文伯格和莱文伯格·马尔夸特方法，作为特殊情况。此外，提出的增强牛顿方法可以解释为具有自适应重球动量的牛顿方法。我们为在各种问题的轻度假设下为拟议方法提供了全球收敛结果。可以寻求所提出的方法作为Karimireddy等人获得的结果的罚款和增强扩展。 Al [24]。
We propose two variants of Newton method for solving unconstrained minimization problem. Our method leverages optimization techniques such as penalty and augmented Lagrangian method to generate novel variants of the Newton method namely the Penalty Newton method and the Augmented Newton method. In doing so, we recover several well-known existing Newton method variants such as Damped Newton, Levenberg, and Levenberg-Marquardt methods as special cases. Moreover, the proposed Augmented Newton method can be interpreted as Newton method with adaptive heavy ball momentum. We provide global convergence results for the proposed methods under mild assumptions that hold for a wide variety of problems. The proposed methods can be sought as the penalty and augmented extensions of the results obtained by Karimireddy et. al [24].
