多元函数条件极值的必要条件  

Necessary Conditions for Constrained Extreme Value of Tri-Function

作　　者：张冬燕[1] 王耀革[1] 张武军[1] 

机构地区：[1]解放军信息工程大学理学院,郑州450000

出　　处：《大学数学》2015年第5期98-103,共6页College Mathematics

摘　　要：推导证明了一般n元函数及常用的二元、三元函数在等式约束条件下用行列式表示的极值的必要条件,并从几何上对二元、三元函数在等式约束条件下取极值的必要条件予以了直观解释.利用这些必要条件求解条件极值,因除去了Lagrange乘数法带来的Lagrange乘子对解方程组的困扰,而使得最终方程组的求解变得明快简洁.The paper provides an entire derivation of necessary conditions represented by determinant for conditional extreme value of multivariate function , binary function and ternary function under the equality constraints . And geometrical interpretations are presented to explain the necessary conditions for conditional extreme value of binary , ternary function .These necessary conditions simplify the solution of the constrained extreme value problem as they avoid the interference of Lagrange multiplicator in solving the final equation .

关 键 词：多元函数 条件极值 必要条件 

分 类 号：O172[理学—数学]