最速下降法的一次迭代收敛性的一点注记  

A Note on the One Step Termination for the Steepest Descent Method

作　　者：邱松强 谢海燕 QIU Songqiang;XIE Haiyan(China University of Mining and Technology,School of Mathematics,Xuzhou Jiangsu 221116,China;Jiangsu Normal University,School of Mathematics and Statistics,Xuzhou Jiangsu 221116,China)

机构地区：[1]中国矿业大学数学学院,江苏徐州221116 [2]江苏师范大学数学与统计学院,江苏徐州221116

出　　处：《大学数学》2023年第6期53-56,共4页College Mathematics

基　　金：中国矿业大学教学研究项目(2020YB42)。

摘　　要：推广了最速下降法经过一次迭代到达严格凸二次规划问题的最优解的充分必要条件:初始点可以表示为最优解和Hesse矩阵的一个特征向量之和.证明此条件也是最速下降法经过有限次迭代后到达最优解的充要条件.丰富了最速下降法的理论,有助于更好地认识和理解最速下降法,对相关算法的教学有一定的启发意义.A well-known property of the steepest descent method for unconstrained convex quadratic programming:if the initial point can be represented as a combination of the minimum and an eigenvector,then it will reach the solution in one iteration.We show that this condition is also a sufficient and necessary condition of finite-step termination of the steepest descent method.This work can help the students to get better understand of steepest descent method.

关 键 词：最速下降法 一次迭代收敛性 特征值 特征向量 

分 类 号：O221.2[理学—运筹学与控制论]