Fixlets to the example.

Signed-off-by: Jérôme Benoit <jerome.benoit@piment-noir.org>

diff --git a/rapport/ProjetOptimRO.tex b/rapport/ProjetOptimRO.tex
index 925282d2a45275e67294752a0bb5310badd8fa57..bd12bfa7b51a638c6e57cacf20b138a453d7e996 100644 (file)
--- a/rapport/ProjetOptimRO.tex
+++ b/rapport/ProjetOptimRO.tex
@@ -761,7 +761,7 @@ $$
 où $$ (r,r_1,r_2) \in \mathbb{R}_+^3. $$
 Les hypothèses : $ J $ et $ g $ sont de classe $ \mathcal{C}^2 $.
 \newline
 où $$ (r,r_1,r_2) \in \mathbb{R}_+^3. $$
 Les hypothèses : $ J $ et $ g $ sont de classe $ \mathcal{C}^2 $.
 \newline

-Le Lagrangien de $ \mathcal(P) $ : $ L(x,y,z,\lambda) = $
+Le Lagrangien de $ \mathcal{P} $ : $ L(x,y,z,\lambda) = $

 \newline
 Le gradient de $ J $ : $ \nabla J(x,y,z) = (\frac{\partial J}{\partial x}(x,y,z),\frac{\partial J}{\partial y}(x,y,z),\frac{\partial J}{\partial z}(x,y,z)) = $
 \newline
 \newline
 Le gradient de $ J $ : $ \nabla J(x,y,z) = (\frac{\partial J}{\partial x}(x,y,z),\frac{\partial J}{\partial y}(x,y,z),\frac{\partial J}{\partial z}(x,y,z)) = $
 \newline


@@ -769,9 +769,9 @@ Le gradient de $ g $ : $ \nabla g(x,y,z) = (\nabla g_1(x,y,z),\nabla g_2(x,z,z))
 \newline
 La matrice hessienne de $ J $ : $ H[J](x,y,z) =
  \begin{pmatrix}
 \newline
 La matrice hessienne de $ J $ : $ H[J](x,y,z) =
  \begin{pmatrix}

-  \frac{\partial^2 J}{\partial^2 x}         & \frac{\partial^2 J}{\partial x\partial y} & \frac{\partial^2 J}{\partial x\partial z} \\
-  \frac{\partial^2 J}{\partial y\partial x} & \frac{\partial^2 J}{\partial^2 y}         & \frac{\partial^2 J}{\partial y\partial z} \\
-  \frac{\partial^2 J}{\partial z\partial x} & \frac{\partial^2 J}{\partial z\partial y} & \frac{\partial^2 J}{\partial^2 z}         \\
+  \frac{\partial^2 J}{\partial^2 x}(x,y,z)         & \frac{\partial^2 J}{\partial x\partial y}(x,y,z) & \frac{\partial^2 J}{\partial x\partial z}(x,y,z) \\
+  \frac{\partial^2 J}{\partial y\partial x}(x,y,z) & \frac{\partial^2 J}{\partial^2 y}(x,y,z)         & \frac{\partial^2 J}{\partial y\partial z}(x,y,z) \\
+  \frac{\partial^2 J}{\partial z\partial x}(x,y,z) & \frac{\partial^2 J}{\partial z\partial y}(x,y,z) & \frac{\partial^2 J}{\partial^2 z}(x,y,z)         \\

  \end{pmatrix} =
  \begin{pmatrix}
    &  & \\
  \end{pmatrix} =
  \begin{pmatrix}
    &  & \\