  This paper concerns a class of DC composite optimization problems which, as
an extension of convex composite optimization problems and DC programs with
nonsmooth components, often arises in robust factorization models of low-rank
matrix recovery. For this class of nonconvex and nonsmooth problems, we propose
an inexact linearized proximal algorithm (iLPA) by computing in each step an
inexact minimizer of a strongly convex majorization constructed with a partial
linearization of their objective functions at the current iterate, and
establish the convergence of the generated iterate sequence under the
Kurdyka-\L\"ojasiewicz (KL) property of a potential function. In particular, by
leveraging the composite structure, we provide a verifiable condition for the
potential function to have the KL property of exponent $1/2$ at the limit
point, so for the iterate sequence to have a local R-linear convergence rate.
Finally, we apply the proposed iLPA to a robust factorization model for matrix
completions with outliers and non-uniform sampling, and numerical comparison
with a proximal alternating minimization (PAM) method confirms iLPA yields the
comparable relative errors or NMAEs within less running time, especially for
large-scale real data.
