A popular approach to solve a large scale optimization problem under independent constraints is to cyclically update a subset of variables by minimizing a locally tight convex upper bound of the original (possibly nonsmooth) cost function.This approach includes the well-known block coordinate descent method (BCD),the block coordinate proximal point method (BCD) and the expectation maximization (EM) method,among others.In this work,we establish the convergence of the method under mild assumptions on the convex upper bound used at each iteration.Our work unifies,extends and strengthens the existing convergence analysis of the BCD and the EM method,and can be used to derive the convergence of block successive upper minimization methods for tensor decomposition,linear transceiver design in wireless networks,and DC (difference of convex functions) programming,among others.