  In this note, we consider the line search for a class of abstract nonconvex
algorithm which have been deeply studied in the Kurdyka-Lojasiewicz theory. We
provide a weak convergence result of the line search in general. When the
objective function satisfies the Kurdyka-Lojasiewicz property and some certain
assumption, a global convergence result can be derived. An application is
presented for the L0-regularized least square minimization in the end of the
paper.
