  This paper deals with the analysis of a recent reformulation of the
primal-dual hybrid gradient method [Zhu and Chan 2008, Pock, Cremers, Bischof
and Chambolle 2009, Esser, Zhang and Chan 2010, Chambolle and Pock 2011], which
allows to apply it to nonconvex regularizers as first proposed for truncated
quadratic penalization in [Strekalovskiy and Cremers 2014]. Particularly, it
investigates variational problems for which the energy to be minimized can be
written as $G(u) + F(Ku)$, where $G$ is convex, $F$ semiconvex, and $K$ is a
linear operator. We study the method and prove convergence in the case where
the nonconvexity of $F$ is compensated by the strong convexity of the $G$. The
convergence proof yields an interesting requirement for the choice of algorithm
parameters, which we show to not only be sufficient, but necessary.
Additionally, we show boundedness of the iterates under much weaker conditions.
Finally, we demonstrate effectiveness and convergence of the algorithm beyond
the theoretical guarantees in several numerical experiments.
