  Semi-continuous decision variables arise naturally in many real-world
applications. They are defined to take either value zero or any value within a
specified range, and occur mainly to prevent small nonzero values in the
solution. One particular challenge that can come with semi-continuous variables
in practical models is that their upper bound may be large or even infinite. In
this article, we briefly discuss these challenges, and present a new diving
heuristic tailored for mixed-integer optimization problems with general
semi-continuous variables. The heuristic is designed to work independently of
whether the semi-continuous variables are bounded from above, and thus
circumvents the specific difficulties that come with unbounded semi-continuous
variables. We conduct extensive computational experiments on three different
test sets, integrating the heuristic in an open-source MIP solver. The results
indicate that this heuristic is a successful tool for finding high-quality
solutions in negligible time. At the root node the primal gap is reduced by an
average of 5 % up to 21 %, and considering the overall performance improvement,
the primal integral is reduced by 2 % to 17 % on average.
