Lagrange乘数法的几何直观推导  

Lagrange Multiplier Method Introduced from View of Geometry

作　　者：刘三明[1] 李修勇[2] 

机构地区：[1]江苏科技大学数理系,江苏镇江212003 [2]河南科技大学数理系,河南洛阳471003

出　　处：《河南科技大学学报（自然科学版）》2004年第6期82-84,共3页Journal of Henan University of Science And Technology:Natural Science

基　　金：江苏省教育厅基金资助项目(JH02-048)

摘　　要：从几何上,直观地介绍求解一类条件极值问题的Lagrange乘数法,显得很形象、易于理解。另外,用Lagrange乘数法求出的解不一定是条件极值问题的极小值解。利用二阶导数给出了用Lagrange乘数法求出的解是条件极值问题的极小值解的一个充分条件。用该条件判别,比用已有的方法判别简单易行。The Lagrange multiplier method is derived from the view of geometry. Furthermore, the solutions given by the Lagrange multiplier method are not necessarily minimal solutions about the conditional extremum problem. A sufficient condition of second order is given for that solutions given by the Lagrange multiplier method are minimal solutions of the conditional extremum problem. When this second order sufficient condition is used for a judgment method, it is more convenient than other judgment methods.

关 键 词：LAGRANGE乘数法 几何直观 极小值 推导 充分条件 二阶导数 求解 条件极值问题 理解 形象 

分 类 号：G633[文化科学—教育学] O178[理学—数学]