Convex Optimization

Gradient && Hessian The gradient of a f, d x 1, can be represented as follow $$\nabla f(x) = \begin{bmatrix} \frac {\partial f(x)} {\partial x_1} \newline …\newline \frac {\partial f(x)} {\partial x_d} \end{bmatrix}$$ and the Hessian, d x d, can be represented as $$\nabla^2 f(x) = \begin{bmatrix} \frac {\partial^2 f(x)} {\partial x_1^2} & \frac {\partial^2 f(x)} {\partial x_1x_2} & \frac {\partial^2 f(x)} {\partial x_1x_d} \newline … & … & …\newline \frac {\partial^2 f(x)} {\partial x_d^2} & \frac {\partial^2 f(x)} {\partial x_dx_2} & \frac {\partial^2 f(x)} {\partial x_dx_d} \newline \end{bmatrix}$$ ……

Read More