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In this paper, we present a semi-proximal alternating direction method ofmultipliers (ADMM) for solving $3$-block separable convex minimization problemswith the second block in the objective being a strongly convex function and onecoupled linear equation constraint. By choosing the semi-proximal termsproperly, we establish the global convergence of the proposed semi-proximalADMM for the step-length $\tau \in (0, (1+\sqrt{5})/2)$ and the penaltyparameter $\sigma\in (0, +\infty)$. In particular, if $\sigma>0$ is smallerthan a certain threshold and the first and third linear operators in the linearequation constraint are injective, then all the three added semi-proximal termscan be dropped and consequently, the convergent $3$-block semi-proximal ADMMreduces to the directly extended $3$-block ADMM with $\tau \in (0,(1+\sqrt{5})/2)$.

A Convergent $3$-Block Semi-Proximal ADMM for Convex Minimization Problems with One Strongly Convex Block