From 46973afbb2be010f0e7732f29b7d7c79c002568e Mon Sep 17 00:00:00 2001 From: =?utf8?q?J=C3=A9r=C3=B4me=20Benoit?= Date: Tue, 6 Nov 2018 21:11:01 +0100 Subject: [PATCH] Fixlets to the example. MIME-Version: 1.0 Content-Type: text/plain; charset=utf8 Content-Transfer-Encoding: 8bit Signed-off-by: Jérôme Benoit --- rapport/ProjetOptimRO.tex | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) 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} & & \\ -- 2.34.1