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We introduce and analyze BPALM and A-BPALM, two multi-block proximalalternating linearized minimization algorithms using Bregman distances forsolving structured nonconvex problems. The objective function is the sum of amulti-block relatively smooth function (i.e., relatively smooth by fixing allthe blocks except one) and block separable (nonsmooth) nonconvex functions. Itturns out that the sequences generated by our algorithms are subsequentiallyconvergent to critical points of the objective function, while they areglobally convergent under KL inequality assumption. Further, the rate ofconvergence is further analyzed for functions satisfying the {\L}ojasiewicz'sgradient inequality. We apply this framework to orthogonal nonnegative matrixfactorization (ONMF) that satisfies all of our assumptions and the relatedsubproblems are solved in closed forms, where some preliminary numericalresults is reported.

Multi-block Bregman proximal alternating linearized minimization and its application to orthogonal nonnegative matrix factorization