Modified alternating direction method of multipliers for convex quadratic semidefinite programming

A three-operator splitting perspective of a three-block ADMM for convex quadratic semidefinite programming and extensions

“…[3] for a concrete example). Therefore, attentions have been paid to the design of multi-block ADMM-type algorithms and, fortunately, several algorithms of this type have been successfully applied to solving the CQSDP problem via its dual with a satisfactory numerical efficiency and a theoretical guarantee of convergence [1,4,14].…”

“…Among of these ADMM-type algorithms for CQSDP problems, the modified 3-block ADMM by Chang et al [1] has a distinct feature that one of the subproblems, i.e., the minimization of the augmented Lagrangian function with respect to a certain block of variables, can always be skipped. This saves both the computational cost and the memory for variable storage, and, more importantly, the convergence is guaranteed under only one extra condition on the penalty parameter σ, while the proof for the convergence is much more involved.…”

“…We mention that for a recent survey on this topic one may refer to [8], and one also can refer to [26] and references therein for more details and recent progresses on generalized ADMM. Consequently, we are interested if one can also interpret the modified 3-block ADMM in [1] via a certain operator splitting scheme and get further improvements on this algorithm via certain over-relaxation steps.…”

“…In this paper, we fulfil our objective by showing that the modified 3-block ADMM in [1] can be explained as an application of the 3-operator splitting framework studied in Davis and Yin [6]. We conduct our analysis in a much general setting in which the model that we will consider contains the CQSDP problem as a special case.…”

“…The remaining parts of this paper are organized as follows. In Section 2, we give a quick review of the CQSDP problem and the modified 3-block ADMM algorithm proposed by Chang et al [1]. Section 3 is devoted to the operator-splitting perspective of this modified 3-block ADMM for the CQSDP problem.…”