  The linearly constrained convex composite programming problems whose
objective function contains two blocks with each block being the form of
nonsmooth+smooth arises frequently in multiple fields of applications. If both
of the smooth terms are quadratic, this problem can be solved efficiently by
using the symmetric Gaussian-Seidel (sGS) technique based proximal alternating
direction method of multipliers (ADMM). However, in the non-quadratic case, the
sGS technique can not be used any more, which leads to the separable structure
of nonsmooth+smooth had to be ignored. In this paper, we present a generalized
ADMM and particularly use a majorization technique to make the corresponding
subproblems more amenable to efficient computations. Under some appropriate
conditions, we prove its global convergence for the relaxation factor in
$(0,2)$. We apply the algorithm to solve a kind of simulated convex composite
optimization problems and a type of sparse inverse covariance matrix estimation
problems which illustrates that the effectiveness of the algorithm are obvious.
