求可测函数的总体极小值方法的收敛性分析

Convergence Analysis for Solving Global Optimization of Measure Function

文[1]中提出了求解连续函数f(z)总体极小值的均值算法,并证明了算法的全局收敛性.若假设f(z)是定义在某可测集G上的可测函数,本文证明了均值算法产生的迭代序列全局收敛到f(x)的本质极小值,若进一步假设函数f(z)满足测度Lipschitz条件,还证明了求可测函数的均值算法是线性收敛的.

Zheng Quan etc Present a mean method for solving global optimization problems in [1], If the objective function is continuous, they prove the global convergence of the mean method- In this paper, we discuss the linear convergence of mean method for global optimization problems, if the objective function is measurable and satisfies measure Lipschitz condition.