  This paper is concerned with the column $\ell_{2,0}$-regularized
factorization model of low-rank matrix recovery problems and its computation.
The column $\ell_{2,0}$-norm of factor matrices is introduced to promote column
sparsity of factors and low-rank solutions. For this nonconvex discontinuous
optimization problem, we develop an alternating majorization-minimization (AMM)
method with extrapolation, and a hybrid AMM in which a majorized alternating
proximal method is proposed to seek an initial factor pair with less nonzero
columns and the AMM with extrapolation is then employed to minimize of a smooth
nonconvex loss. We provide the global convergence analysis for the proposed AMM
methods and apply them to the matrix completion problem with non-uniform
sampling schemes. Numerical experiments are conducted with synthetic and real
data examples, and comparison results with the nuclear-norm regularized
factorization model and the max-norm regularized convex model show that the
column $\ell_{2,0}$-regularized factorization model has an advantage in
offering solutions of lower error and rank within less time.
