基于惯性动力系统的加速梯度算法  

Accelerated gradient algorithm based on dynamic inertial system

作　　者：李春凯 LI Chun-kai(School of Science,Beijing University of Posts and Telecommunications,Beijing 100876,China)

机构地区：[1]北京邮电大学理学院,北京100876

出　　处：《哈尔滨商业大学学报（自然科学版）》2021年第6期745-752,共8页Journal of Harbin University of Commerce：Natural Sciences Edition

基　　金：国家自然科学基金面上项目(No.11971073)。

摘　　要：加速梯度算法是指在仅使用一阶梯度信息的前提下,比传统的梯度下降法有更快收敛速率的算法.针对二阶惯性动力系统,采用三种离散格式:辛格式、显式Euler及隐式Euler,分别对系统进行离散化,得到了三种不同的优化算法,通过构造了合适的Lyapunov函数,证明了由辛格式和隐式Euler得到的优化算法是加速梯度算法.Accelerated gradient algorithm is an algorithm which has faster convergence rate than traditional gradient descent method on the premise of using only one step information.In this paper,three discreted schemes:symplectic scheme,explicit Euler and implicit Euler,were used to discretize the second-order dynamic inertial system,and three different optimization algorithms were obtained.By constructing suitable Lyapunov function,it was proved that the optimization algorithms obtained by symplectic scheme and implicit Euler were accelerated gradient algorithms.

关 键 词：惯性动力系统 离散化 LYAPUNOV函数 加速梯度算法 收敛速率 辛格式 

分 类 号：O22[理学—运筹学与控制论]