A convergent 3-block semi-proximal ADMM for convex minimization problems with one strongly convex block

© 2015 World Scientific Publishing Co. & Operational Research Society of Singapore. In this paper, we present a semi-proximal alternating direction method of multipliers (sPADMM) 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 sPADMM for the step-length ? ? (0, (1+5)/2) and the penalty parameter ? (0, +?). In particular, if ? > 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 sPADMM reduces to the directly extended 3-block ADMM with ? ? (0, (1+5)/2).