一个新的条件极值的充分条件

A New Sufficient Condition of Conditional Extreme Value

李文学用拉格朗日函数提出求条件极值的充分条件,但他的证明却是错误的。不仅如此,李氏的充分条件要求过高,一般函数难以满足,这妨碍了充分条件的应用。本文不用拉格朗日函数,而是直接通过消去一个变量将条件极值转化成无条件极值,重新推导出充分性条件,并提出一个新的充分性条件。

Li Wen-xue puts forward a sufficient condition of conditional extreme value with Lagrange Function,but his proof is wrong.Not only this,the sufficient condition which Li Wen-xue presents has too high condition that common function could not satisfy,so it limits its application.This paper derives out the sufficient condition again and suggests a new sufficient condition of conditional extreme value by eliminating a variable from the restricted equation and changing conditional extreme value into the unconditional extreme value instead of using Lagrange Function.