几种多元函数条件极值的解法之比较  

Comparison of Several Solutions to the Conditional Extrema of Multivariable Functions

作　　者：朱江红[1] 孙兰香[1] 

机构地区：[1]沧州师范学院数学系,河北沧州061001

出　　处：《沧州师范学院学报》2010年第2期95-97,共3页Journal of Cangzhou Normal University

摘　　要：多元函数的条件极值是数学分析和高等数学中的一个重要内容,它的一般求解方法为拉格朗日乘数法。给出了四种求多元函数条件极值的方法并比较了适用的条件及难易程度,以便在求解类似的问题时选择适当的方法。The conditional extrema of multivariable functions is an important content in Mathematical Analysis and Advanced Mathematics.Its solution method is generally by Largrange scale multiplication.In this paper,four solutions to find the conditional extrema have given out and their applicable conditions as well as the degrees of difficulty have also been compared for the sake of choosing the right method to solve the similar problems.

关 键 词：条件极值 柯西不等式 均值不等式 拉格朗日乘数法 梯度 

分 类 号：O174.1[理学—数学]