多元函数条件极值的充分条件探讨

Study on the Sufficient Condition of Conditional Extreme Value of Multivariate Function

多元函数条件极值问题,在生活中已有广泛的应用。但关于多元函数条件极值判定条件方面的研究很少。针对此问题,本文给出了新的求多元函数条件极值方法。首先,运用拉格朗日乘数法求出驻点;然后,运用泰勒展开式及隐函数微分法,计算出多元函数的条件极值的新判别法则。最后是实例验证,研究表明,本文所提出的方法是有效的。

The conditional extremum of multivariate function is widely used in life. However,little research has been done on conditional extremum decision conditions for multivariate functions. In response to this problem,this paper presents a new method for finding the extreme conditions of multivariate function conditions. First,the stagnation point is obtained by using the Lagrangian multiplier method. Then,Taylor＇s expansion and implicit function differential method are used to calculate the new criterion for the conditional extremum of the multivariate function. Finally,examples are given to prove that this method is more effective.