\( H(f) = \begin{bmatrix}\frac{\partial^2 f}{\partial x_1^2} & \frac{\partial^2 f}{\partial x_1\,\partial x_2} & \cdots & \frac{\partial^2 f}{\partial x_1\,\partial x_n} \\ \\\frac{\partial^2 f}{\partial x_2\,\partial x_1} & \frac{\partial^2 f}{\partial x_2^2} & \cdots & \frac{\partial^2 f}{\partial x_2\,\partial x_n} \\ \\\vdots & \vdots & \ddots & \vdots \\ \\\frac{\partial^2 f}{\partial x_n\,\partial x_1} & \frac{\partial^2 f}{\partial x_n\,\partial x_2} & \cdots & \frac{\partial^2 f}{\partial x_n^2}\end{bmatrix} \)
En de Laplace operator is de scalar gedefinieerd als:
\( { \nabla }^2 f = \sum_{i=1}^n \frac {\partial^2 f}{\partial x^2_i} \)
Nu staat in mijn cursus het volgende:
A general Quadratic Program can be formulated as follows.
\({\mbox{minimize}}_{x \in { \mathbb{R}}^n} \ \ f(x)=c^T x+ \frac{1}{2} x^T Bx\)\(\mbox{subject to} \ \ Ax-b=0, \ \ Cx-d \geq 0 \)\(B\)is called the "Hessian matrix", it namely stems from the fact that\( {\nabla}^2 f(x)=B\)
Kan iemand hier verduidelijking in scheppen?
