  The alternating direction method of multipliers (ADMM) is a popular method
for solving convex separable minimization problems with linear equality
constraints. The generalization of the two-block ADMM to the three-block ADMM
is not trivial since the three-block ADMM is not convergence in general. Many
variants of three-block ADMM have been developed with guarantee convergence.
Besides the ADMM, the alternating minimization algorithm (AMA) is also an
important algorithm for solving the convex separable minimization problem with
linear equality constraints. The AMA is first proposed by Tseng, and it is
equivalent to the forward-backward splitting algorithm applied to the
corresponding dual problem. In this paper, we design a variant of three-block
AMA, which is derived by employing an inertial extension of the three-operator
splitting algorithm to the dual problem. Compared with three-block ADMM, the
first subproblem of the proposed algorithm only minimizing the Lagrangian
function. As a by-product, we obtain a relaxed algorithm of Davis and Yin.
Under mild conditions on the parameters, we establish the convergence of the
proposed algorithm in infinite-dimensional Hilbert spaces. Finally, we conduct
numerical experiments on the stable principal component pursuit (SPCP) to
verify the efficiency and effectiveness of the proposed algorithm.
