  In this paper, we propose a generalized alternating direction method of
multipliers (ADMM) with semi-proximal terms for solving a class of convex
composite conic optimization problems, of which some are high-dimensional, to
moderate accuracy. Our primary motivation is that this method, together with
properly chosen semi-proximal terms, such as those generated by the recent
advance of symmetric Gauss-Seidel technique, is applicable to tackling these
problems. Moreover, the proposed method, which relaxes both the primal and the
dual variables in a natural way with one relaxation factor in the interval
$(0,2)$, has the potential of enhancing the performance of the classic ADMM.
Extensive numerical experiments on various doubly non-negative semidefinite
programming problems, with or without inequality constraints, are conducted.
The corresponding results showed that all these multi-block problems can be
successively solved, and the advantage of using the relaxation step is
apparent.

Optimization and Control