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= Reverse-Huber penalty
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The Berhu, or reverse-Huber, penalty with threshold $\delta>0$ is
$$
\rho_\delta(t)=
\begin{cases}
|t|,&|t|\leq\delta,\\
(t^2+\delta^2)/(2\delta),&|t|>\delta.
\end{cases}
$$
It behaves like the <absolute value> near zero and quadratically for large coefficients.

Berhu penalty

Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 205 / 4 / Solution

Berhu penalty

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Berhu penalty

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