I'm trying to prove the convergence of Matrix factorization. The problem is described below. $|X-WH|^2 + |H|_2^2 +|W|_2^2$.
My optimization steps are using Alternating least squares which update H with fixing W and update W with fixing H.
Although I can prove the convergence of subproblems(e.x. update H with fixing W), I have no idea to prove the convergence of this problem but not subproblems.
Does someone give some clues about how to prove the convergence of matrix factorization globally?
Thanks.