B. Optimization

$\vec{x} \in \mathbb{R}^{n}$ is a real vector with n components, $f(\vec{x})$ is a scalar function dependent of the vector $\vec{x}$, while $\vec{f}(\vec{x})$ is a vector values function. Uppercase letters denote matrices of real numbers, for example $\mathcal{A} \in \mathbb{R}^{m \times n}$ is an m x n real matrix.