  We consider a multi-block separable convex optimization problem with the
linear constraints, where the objective function is the sum of m individual
convex functions without overlapping variables. The linearized version of the
generalized alternating direction method of multipliers (L-GADMM) is
particularly efficient for the two-block separable convex programming problem
and its convergence was proved when two blocks of variables are alternatively
updated. However,the convergence and some practical applications of the
extension (m>=3) of the L-GADMM is still in its infancy. In this paper, we
extend this algorithm to the general case where the objective function consists
of the sum of m-block convex functions. Theoretically, we prove global
convergence of the new method and establish the worst-case convergence rate in
the ergodic and nonergodic senses for the proposed algorithm. The efficiency of
the new method is further demonstrated through numerical results on the
calibration of the correlation matrices.
