In this paper, we consider block-decomposition first-order methods for solving large-scale conic semidefinite programming problems. Several ingredients are introduced to speed-up the method in its pure form such as: an aggressive choice of stepsize for performing the extragradient step; use of scaled inner products in the primal and dual spaces; dynamic update of the scaled inner product in the primal space for properly balancing the primal and dual relative residuals; and proper choices of the initial primal and dual iterates, as well as the initial parameter for the primal scaled inner product. Finally, we present computational results showing that our method outperforms the two most competitive codes for large-scale conic semidefinite programs, namely: the boundary point method introduced by Povh et al. and the Newton-CG augmented Lagrangian method by Zhao et al.
School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0205, USA, May, 2011