| Function | Meaning | Domain | Sign | Curvature | Monotonicity |
| abs(x) | $ |x| $ | $ x \in \mathbf{R} $ |  positive |
 convex |
|
| entr(x) | $ \begin{cases} -x \log (x) & x > 0 \\ 0 & x = 0 \end{cases} $ | $ x \geq 0 $ |  unknown |
 concave |
None |
| exp(x) | $ e^{x} $ | $ x \in \mathbf{R} $ | positive |
convex |
|
| geo_mean(x1,...,xk) | $ (x_{1} \cdots x_{k})^{1/k} $ | $ x_{i} \geq 0 $ | positive |
concave |
|
| huber(x) | $ \begin{cases} 2|x|-1 & |x| \ge 1 \\ |x|^{2} & |x| < 1 \end{cases} $ | $ x \in \mathbf{R} $ | positive |
convex |
|
| inv_pos(x) | $ 1/x $ | $ x > 0 $ | positive |
convex |
|
| kl_div(x,y) | $ x \log (x/y)-x+y $ | $ x,y > 0 $ | positive |
convex |
None |
| log(x) | $ \log(x) $ | $ x > 0 $ | unknown |
concave |
|
| log_sum_exp(x1,...,xk) | $ \log \left(e^{x_{1}} + \cdots + e^{x_{k}} \right) $ | $ x \in \mathbf{R}^{k} $ | unknown |
convex |
|
| max(x1,...,xk) | $ \max \left\{ x_{1}, \ldots , x_{k} \right\} $ | $ x \in \mathbf{R}^{k} $ | max(sign(arguments)) | convex |
|
| min(x1,...,xk) | $ \min \left\{ x_{1}, \ldots , x_{k} \right\} $ | $ x \in \mathbf{R}^{k} $ | min(sign(arguments)) | concave |
|
| norm2(x1,...,xk) | $ \sqrt{x_{1}^{2} + \cdots + x_{k}^{2}} $ | $ x \in \mathbf{R}^{k} $ | positive |
convex |
|
| norm1(x1,...,xk) | $ |x_{1}| + \cdots + |x_{k}| $ | $ x \in \mathbf{R}^{k} $ | positive |
convex |
|
| norm_inf(x1,...,xk) | $ \max \left\{ |x_{1}|, \ldots, |x_{k}| \right\} $ | $ x \in \mathbf{R}^{k} $ | positive |
convex |
|
| pos(x) | $ \max \{x,0\} $ | $ x \in \mathbf{R}$ | positive |
convex |
|
| quad_over_lin(x,y) | $ x^{2}/y $ | $x \in \mathbf{R}$, y > 0 | positive |
convex |
|
| sqrt(x) | $ \sqrt{x} $ | $ x \geq 0 $ | positive |
concave |
|
| square(x) | $ x^{2} $ | $ x \in \mathbf{R} $ | positive |
convex |
|
| pow(x,p), $\text{ } p \geq 1 $ | $ x^{p} $ | $ x \geq 0 $ | positive |
convex |
|
| pow(x,p), $\text{ } 0 < p < 1 $ | $ x^{p} $ | $ x \geq 0 $ | positive |
concave |
|
| pow(x,p), $\text{ } p \leq 0 $ | $ x^{p} $ | $ x > 0 $ | positive |
convex |
|
incr. for $ x \geq 0 $
decr. for $ x \leq 0 $