X-Git-Url: https://git.piment-noir.org/?a=blobdiff_plain;f=rapport%2FProjetOptimRO.tex;h=11ede70314b3c093cf65427f68e840aa6a0cb095;hb=f472f4dd55de9cbe58c5d3a22c95517d3ced78d3;hp=925282d2a45275e67294752a0bb5310badd8fa57;hpb=7590f4bb3c2432c43c58e6f4480c03bc324d7dfc;p=Projet_Recherche_Operationnelle.git

diff --git a/rapport/ProjetOptimRO.tex b/rapport/ProjetOptimRO.tex
index 925282d..11ede70 100644
--- a/rapport/ProjetOptimRO.tex
+++ b/rapport/ProjetOptimRO.tex
@@ -759,9 +759,9 @@ $$
  \right .
 $$
 où $$ (r,r_1,r_2) \in \mathbb{R}_+^3. $$
-Les hypothèses : $ J $ et $ g $ sont de classe $ \mathcal{C}^2 $.
+\textit{Entrées} : $ J $ et $ g $ de classe $ \mathcal{C}^2 $, $ \varepsilon = 0.01 $ la précision, $ (x_0,y_0,z_0) = $ point initial et $ \lambda_0 = $ multiplicateur initial.
 \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
@@ -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}
-  \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}
    &  & \\