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I am doing an optimization using Newton-Raphson, when I am setting the initial values of the parameter vector that makes the Hessian matrix is negative semi-definite as necessary condition for maximal point, i got a Hessian matrix with negative diagonal elements. The sign of those elements should be positive??

N. I. ElZayat
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  • Let us take a simple example, $f(x)=-x^2$. (Or $f(x,y)=-x^2-y^2 if we want a "true matrix"...) Which is the second derivative / the Hessian, is it negative definite, do we have a maximum (in the origin)? – dan_fulea May 06 '18 at 14:38
  • Thanks Dan for replying, my question mainly ask about the sign of the off diagonal elements of the Hessian matrix in apart from using it to check the critical point is maximum or minimum. – N. I. ElZayat May 06 '18 at 22:36
  • And i gave an explicit example which has obviously a maximum in $0$, resp $(0,0)$, where the Hessian is the $1\times 1$ matrix $[-2]$, resp. the matrix $\begin{bmatrix}-2&0\0&-2\end{bmatrix}$. The example should make clear how to decode the diagonal signs as maximum / minimum. – dan_fulea May 07 '18 at 08:28
  • Okay , I got it tanks – N. I. ElZayat May 07 '18 at 12:20

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