A majorized PAM method with subspace correction for low-rank composite factorization model
arxiv(2024)
Abstract
This paper concerns a class of low-rank composite factorization models
arising from matrix completion. For this nonconvex and nonsmooth optimization
problem, we propose a proximal alternating minimization algorithm (PAMA) with
subspace correction, in which a subspace correction step is imposed on every
proximal subproblem so as to guarantee that the corrected proximal subproblem
has a closed-form solution. For this subspace correction PAMA, we prove the
subsequence convergence of the iterate sequence, and establish the convergence
of the whole iterate sequence and the column subspace sequences of factor pairs
under the KL property of objective function and a restrictive condition that
holds automatically for the column ℓ_2,0-norm function. Numerical
comparison with the proximal alternating linearized minimization method on
one-bit matrix completion problems indicates that PAMA has an advantage in
seeking lower relative error within less time.
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