3 research outputs found
A Convergent -Block Semi-Proximal ADMM for Convex Minimization Problems with One Strongly Convex Block
In this paper, we present a semi-proximal alternating direction method of
multipliers (ADMM) for solving -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 and the penalty
parameter . In particular, if 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 -block semi-proximal ADMM
reduces to the directly extended -block ADMM with .Comment: 15 page