(a) Solution set of quadratic inequality, i.e., $\{x \in \mathbb{R}^{n} \:\mid\: x^{\top}Ax + b^{\top}x + c \leq 0, \quad A\in\mathbb{S}^{n}_{+}, \quad b\in\mathbb{R}^{n}, \quad c\in\mathbb{R} \}$.
(b) Hyperbolic set, i.e., $\{x \in \mathbb{R}^{n}_{+} \: \mid \: \displaystyle\prod_{i=1}^{n}x_{i} \geq 1\}.$
(c) A slab, i.e., $\{x \in \mathbb{R}^{n} \:\mid\: \alpha \leq a^{\top}x \leq \beta, \quad a\in\mathbb{R}^{n}, \quad \alpha,\beta\in\mathbb{R}\}$.
(d) A rectangle, i.e., $\{x\in \mathbb{R}^{n}\:\mid\: \alpha \leq x \leq \beta, \quad \alpha,\beta\in\mathbb{R}^{n}, \quad \text{vector inequality is elementwise}\}$.
(e) A wedge, i.e., $\{x\in\mathbb{R}^{n} \:\mid\: a_{1}^{\top}x \leq b_{1}, \quad a_{2}^{\top}x \leq b_{2}, \quad a_{1},a_{2}\in\mathbb{R}^{n}, \quad b_{1},b_{2}\in\mathbb{R}\}$.
(f) Set of points closer to a given point than a given set, i.e., $\{x\in\mathbb{R}^{n} \:\mid\: \parallel x - x_{0}\parallel_{2} \:\leq\: \parallel x - y\parallel_{2}, \quad \forall\:y\in\mathcal{S}\subseteq\mathbb{R}^{n}, \quad x_{0}\in\mathbb{R}^{n}\}$.
(g) Set of points closer to one set than another, i.e., $\{x\in\mathbb{R}^{n} \:\mid\: {\rm{dist}}(x,\mathcal{S})\leq {\rm{dist}}(x,\mathcal{T}), \quad \mathcal{S},\mathcal{T}\subseteq\mathbb{R}^{n}\},\quad$and$\quad{\rm{dist}}(x,\mathcal{S}) := \inf\{\parallel x - z \parallel_{2} \:\mid\: z\in\mathcal{S}\}$.
(h) Subtraction from a convex set, i.e., $\{x\in\mathbb{R}^{n} \:\mid\: x +\mathcal{S}_{2} \subseteq \mathcal{S}_{1}, \quad \mathcal{S}_{1},\mathcal{S}_{2}\subseteq\mathbb{R}^{n}, \quad \mathcal{S}_{1}\,\text{convex}\}$.
(i) Set of points whose distance to a given point ($a\in\mathbb{R}^{n}$) does not exceed a fixed fraction ($0\leq \theta\leq 1$) of the distance to another given point ($b\in\mathbb{R}^{n}$), i.e., $\{x\in\mathbb{R}^{n} \:\mid\: \parallel x - a \parallel_{2} \:\leq\: \theta\parallel x - b \parallel_{2}, \quad a\neq b\}$.
(j) Expansion of a convex set by $a\geq 0$, i.e., $\{x\in\mathbb{R}^{n} \:\mid\: {\rm{dist}}(x,\mathcal{S})\leq a, \quad \mathcal{S}\,\text{convex}\}$.