A Note on the Optimal Convergence Rate of Descent Methods with Fixed Step Sizes for Smooth Strongly Convex Functions
基于Taylor等人的结果，本文对光滑强凸函数的固定步长下降法进行了收敛性分析，涵盖变度量法、梯度相关搜索方向和不精确梯度法，并给出了最优收敛速度。
Abstract Based on a result by Taylor et al. (J Optim Theory Appl 178(2):455–476, 2018) on the attainable convergence rate of gradient descent for smooth and strongly convex functions in terms of function values, an elementary convergence analysis for general descent methods with fixed step sizes is presented. It covers general variable metric methods, gradient-related search directions under angle and scaling conditions, as well as inexact gradient methods. In all cases, optimal rates are obtained.