From: Jérôme Benoit Date: Tue, 6 Nov 2018 20:11:01 +0000 (+0100) Subject: Fixlets to the example. X-Git-Url: https://git.piment-noir.org/?a=commitdiff_plain;h=46973afbb2be010f0e7732f29b7d7c79c002568e;p=Projet_Recherche_Operationnelle.git Fixlets to the example. Signed-off-by: Jérôme Benoit --- diff --git a/rapport/ProjetOptimRO.tex b/rapport/ProjetOptimRO.tex index 925282d..bd12bfa 100644 --- 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 -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} & & \\