In this paper, we propose a generalized alternating direction method ofmultipliers (ADMM) with semi-proximal terms for solving a class of convexcomposite conic optimization problems, of which some are high-dimensional, tomoderate accuracy. Our primary motivation is that this method, together withproperly chosen semi-proximal terms, such as those generated by the recentadvance of symmetric Gauss-Seidel technique, is applicable to tackling theseproblems. Moreover, the proposed method, which relaxes both the primal and thedual 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 semidefiniteprogramming problems, with or without inequality constraints, are conducted.The corresponding results showed that all these multi-block problems can besuccessively solved, and the advantage of using the relaxation step isapparent.
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