基于导数张量的多元函数极值点判定

Extreme Point Determination of Multivariate Function Based on Derivative Tensor

针对多元函数极值点判定问题,定义了多元函数的导数张量,给出了张量形式的多元函数带皮亚诺余项的泰勒公式,提出了基于张量的最大和最小Z特征值对多元函数极值点进行判定的方法.

Aiming at the extreme point determination of a multivariate function,we define derivative tensors of a multivariate function,obtain a tensor version of multivariate Taylor’s formula with Peano remainder and propose a method to determine interior extreme points of a multivariate function based on the largest and smallest Z eigenvalues of the tensor.