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

Column $\ell_{2,0}$-norm regularized factorization model of low-rank matrix recovery and its computation