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改错。

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2023-04-22 17:43:53 +08:00
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14多变量函数的微分学.tex
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@@ -540,7 +540,7 @@ J_y \bvec{F} = \begin{bmatrix}
根据这个定理，我们可以引入Lagrange乘数法。定义函数$L: D \times \realnum^m \to \realnum$， 根据这个定理，我们可以引入Lagrange乘数法。定义函数$L: D \times \realnum^m \to \realnum$，
\[L(\bvec{z}, \bvec{\Lambda}) = f(\bvec{z}) + \bvec{\lambda} \Phi(\bvec{z}), (\bvec{z}, \bvec{\Lambda}) \in D \times \realnum^m\] \[L(\bvec{z}, \bvec{\Lambda}) = f(\bvec{z}) + \bvec{\lambda} \Phi(\bvec{z}), (\bvec{z}, \bvec{\Lambda}) \in D \times \realnum^m\]
$L$称为条件极值问题的Lagrange函数，$\bvec{\Lambda}$称为Lagrange乘数/乘子。根据条件极值的表要条件，在条件极值点$\bvec{z}_0 \in D$，存在$\bvec{\Lambda} \in \realnum^m$满足 $L$称为条件极值问题的Lagrange函数，$\bvec{\Lambda}$称为Lagrange乘数/乘子。根据条件极值的必要条件，在条件极值点$\bvec{z}_0 \in D$，存在$\bvec{\Lambda} \in \realnum^m$满足
\[J_{\bvec{z}} L (\bvec{z}_0, \bvec{\Lambda}) = J_{\bvec{z}} f(\bvec{z}_0) + \bvec{\Lambda} J_{\bvec{z}}\Phi(\bvec{z}_0) = \bvec{0}\] \[J_{\bvec{z}} L (\bvec{z}_0, \bvec{\Lambda}) = J_{\bvec{z}} f(\bvec{z}_0) + \bvec{\Lambda} J_{\bvec{z}}\Phi(\bvec{z}_0) = \bvec{0}\]
此外 此外
\[J_{\bvec{\Lambda}} L(\bvec{z}_0, \bvec{\Lambda}) = \Phi(\bvec{z}_0) = \bvec{0}\] \[J_{\bvec{\Lambda}} L(\bvec{z}_0, \bvec{\Lambda}) = \Phi(\bvec{z}_0) = \bvec{0}\]