Differential calculus: Gradient and hessian local minimum point

Asked Apr 25 '17 at 05:57

Active Apr 25 '17 at 05:57

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Let the function defined on E = R$^2$ by J(x,y)=$x^2-xy +y^2+3x-2y+1$

Calculate the associated gradient and hessian? Deduce, the value of a local mimi point is what a strict mimimum

So the gradiant is : $(2x-y+3,2y-x-2)$

$1) 2x-y=-3$ and $2) 2y-x=3$ we can deduce 1) + 2) => y=0 $ and $ x=-1 $ or x=3/2$

J(x,y) -J(0,-1)==$x^2-xy +y^2+3x-2y+1-(1+3+1)=0 $

I made a mistake

asked Apr 25 '17 at 05:57

Paul-henri Guet

You certainly did. A couple of them. What’s your question? – amd Apr 25 '17 at 08:00
My question is to know if the gradient and hessian is true and how to deduce, the value of a local mimi point is what a strict mimimum – Paul-henri Guet Apr 25 '17 at 08:36

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