Lagrange函数的几何引入  

Lagrangian multipler method introduced from geometric point

作　　者：贺慧霞 苑佳 HE Huixia;YUAN Jia(Department of Mathematics,Beihang University,Beijing 100191,China)

机构地区：[1]北京航空航天大学数学科学学院,北京100191

出　　处：《南阳师范学院学报》2021年第6期21-24,44,共5页Journal of Nanyang Normal University

基　　金：北京航空航天大学教改项目;北京航空航天大学校级一流课程建设项目。

摘　　要：多元函数的条件极值问题是数学分析中的一个重要研究内容,它在其他学科领域都有着广泛应用,而且也与我们的日常生活密切相关.多元函数的条件极值除了有极少一部分可以转化为无条件极值求解外,绝大多数都是利用Lagrange乘数法解决的.目前大多数教材都是从可微函数的极值点必为驻点入手,然后构造出Lagrange函数,从逻辑推理上非常严谨,但缺少了几何直观,使Lagrange函数的构造不够自然.本文将从一个实例入手,借助于几何描述,更自然地引入Lagrange函数.The conditional extreme value problem of multivariate functions is an important research content in Mathematical Analysis and Advanced Mathematics.It is widely used in other disciplines,such as optimization and engineering,and is also closely related to our daily life.Except that a few of the conditional extremum of multivariate functions can be transformed into unconditional extremum,most of them are solved by Lagrange multiplier method.At present,most textbooks start with the extreme point of differentiable function must be the stationary point,and then construct Lagrange function.It is logically rigorous,but it lacks geometric intuition,which makes the construction of Lagrange function not natural.This paper will start with an example and introduce Lagrange function more naturally with the help of geometric description.

关 键 词：LAGRANGE乘数法 条件极值 消元法 驻点 

分 类 号：O172.1[理学—数学]