条件极值两种求法的不等价条件分析

Analysis of the Non--Equivalent Conditions for Two Methods to Solve Conditional Extremum Problems

本文说明了求条件极值的代入法与Ｌａｇｒａｎｇｅ乘数法的条件不等价。分析了这种不等价的原因，得到了求一般条件极值时，代入法与Ｌａｇｒａｎｇｅ乘数法均有效、前者无效而后者有效，以及两种方法均无效的各种不同条件．

To solve a conditional extremum problem, the conditions of the two methods:the method of substitution and the lagrange's method of multipliers,is not equivaelent.In this paper, we illustrated this fact and analysed the cause.Transparent conditions are given to judge that the two methods are effective the lagrange's method is effective but the method of substitution is ineffective or both the two methods are ineffective.