利用均值算法求解凸函数极小值的收敛性分析

THE CONVERGENCE ANALYSIS OF CONVEX FUNCTION BY USING MEAN METHOD

郑权等在[1]—[3]中提出了一种求解无约束优化问题的均值算法,若假设目标函数 _f(x)是连续的,还讨论了均值算法的收敛性.若假设f(x)是有界闭集Ω上的凸函数,本文证 明了求解凸函数极小值的均值算法是线性收敛的.

Zheng Quan etc present a mean method for solving unconstrained optimization problems in [1]-[3], if the objective function is continuous, prove convergence of the mean method. If we assume the objective function f(x) is convex in a bounded closed set Ω .in this paper, we discuss the linear convergence of the mean method for solving unconstrained optimization problems.