Inexact block coordinate descent methods with application to the nonnegative matrix factorization

This work is concerned with the cyclic block coordinate descent method, or nonlinear Gauss-Seidel method, where the solution of an optimization problem is achieved by partitioning the variables in blocks and successively minimizing with respect to each block. The properties of the objective function that guarantee the convergence of such alternating scheme have been widely investigated in the literature and it is well known that, without suitable convexity hypotheses, the method may fail to locate the stationary points when more than two blocks of variables are employed.