EFFICIENT METHOD FOR FINDING MINIMUM OF FUNCTION OF SEVERAL-VARIABLES WITHOUT CALCULATING DERIVATIVES
EFFICIENT METHOD FOR FINDING MINIMUM OF FUNCTION OF SEVERAL-VARIABLES WITHOUT CALCULATING DERIVATIVES
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DOI：
10.1093/comjnl/7.2.155
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发表时间：
1964-01-01
期刊：
影响因子：
1.4
通讯作者：
POWELL, MJD
中科院分区：
文献类型：
--
作者：
POWELL, MJD
描述了通过一次改变一个参数来最小化多个变量的函数的众所周知的方法的一个简单变体。这种变化是这样的，当该程序应用于二次型时，它导致选择共轭方向，因此当该方法用于最小化一般函数时，最终收敛速度是快的。进一步的变种完善了该方法，它确保了从一个坏的逼近到最小的收敛速度总是有效的。该方法的实际应用证明是非常令人满意的，并给出了最小化多达20个变量的函数的数值例子。
A simple variation of the well-known method of minimizing a function of several variables by changing one parameter at a time is described. This variation is such that when the procedure is applied to a quadratic form, it causes conjugate directions to be chosen, so the ultimate rate of convergence is fast when the method is used to minimize a general function. A further variation completes the method, and its ensures that the convergence rate from a bad approximation to a minimum is always efficient. Practical applications of the procedure have proved to be very satisfactory, and numerical examples are given in which functions of up to twenty variables are minimized.