p>Let us look at an example to see how this works. Consider the
unit-halfwidth Huber penalty function <span class="math">\(h(x)\)</span>:</p>
<div class="math">
\[\begin{split}h:\mathbf{R}\rightarrow\mathbf{R}, \quad h(x) \triangleq \begin{cases} x^2 &amp; |x| \leq 1 \\ 2|x|-1 &amp; |x| \geq 1 \end{cases}.\end{split}\]</div>
<p>We can express the Huber function in terms of the following family of
convex QPs, parameterized by <span class="math">\(x\)</span>:</p>
<div class="math">
\[\begin{split}\begin{array