  Nowadays, L0 optimization model has shown its superiority when pursuing
sparsity in many areas. For this nonconvex problem, most of the algorithms can
only converge to one of its critical points. In this paper, we consider a
general L0 regularized minimization problem, where the L0 ''norm'' is
composited with a continuous map. Under some mild assumptions, we show that
every critical point of this problem is a local minimizer, which improves the
convergence results of existing algorithms. Surprisingly, this conclusion does
not hold for low rank minimization, a natural matrix extension of L0 ''norm''
of a vector.
