  The proximal generalized alternating direction method of multipliers
(p-GADMM) is substantially efficient for solving convex composite programming
problems of high-dimensional to moderate accuracy. The global convergence of
this method was established by Xiao, Chen & Li [Math. Program. Comput., 2018],
but its convergence rate was not given. One may take it for granted that the
convergence rate could be proved easily by mimicking the proximal ADMM, but we
find the relaxed points will certainly cause many difficulties for theoretical
analysis. In this paper, we devote to exploring its convergence behavior and
show that the sequence generated by p-GADMM possesses Q-linear convergence rate
under some mild conditions. We would like to note that the proximal terms at
the subproblems are required to be positive definite, which is very common in
most practical implementations although it seems to be a bit strong.
