  In this paper, we present a semi-proximal alternating direction method of
multipliers (ADMM) for solving $3$-block separable convex minimization problems
with the second block in the objective being a strongly convex function and one
coupled linear equation constraint. By choosing the semi-proximal terms
properly, we establish the global convergence of the proposed semi-proximal
ADMM for the step-length $\tau \in (0, (1+\sqrt{5})/2)$ and the penalty
parameter $\sigma\in (0, +\infty)$. In particular, if $\sigma>0$ is smaller
than a certain threshold and the first and third linear operators in the linear
equation constraint are injective, then all the three added semi-proximal terms
can be dropped and consequently, the convergent $3$-block semi-proximal ADMM
reduces to the directly extended $3$-block ADMM with $\tau \in (0,
(1+\sqrt{5})/2)$.
