等约束条件下多元函数条件极值的充分条件

等约束条件下多元函数极值的充分条件问题通常是采用二阶微分法来判断,该方法原理虽然简单,但计算量大,尤其是随着变量和约束条件个数的增加,要计算出d2 L并判断出其符号就显得更加困难而不可行。文章用Lagrange乘数法、多元隐函数求导法以及有条件极值化无条件极值的方法推导证明了多元函数极值的充分条件,并给出易于计算且切实可行的方法和定理,从不同的角度做出了理论的探索与尝试。

Sufficient Conditions Of Multivariate Function For Conditional Extreme Value Under The Equality Constraints

Sufficient conditions of multivariate function for conditional extreme value under the equality constraints is usually judge with the method of sufficient second differential,although the principle of the method is simple,but computationally intensive,especially with the number of variables and constraint conditions increase,and want to calculate the d2Land determine the sign becomes more difficult and not feasible.In this paper,by using Lagrange multiplier method,derivation of multivariate implicit function,and the method of conditional extreme reversing unconditional extreme,it has deduced the sufficient conditions of the multi-function extreme,and also presents the theorem as well as a practical method which is easy to calculate,make a theoretical exploration and try from different point of view.