In this paper, we first develop ``economical'' representations for positive semidefinitness of well-structured sparse symmetric matrix. Using the representations, we then reformulate well-structured large-scale semidefinite problems into smooth convex-concave saddle point problems, which can be solved by a Prox-method with efficiency ${\cal O}(\epsilon^{-1})$ developed in \cite{Nem}. Some numerical implementations for large-scale Lovasz capacity and MAXCUT problems are finally present.
Citation
Technical report, School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, USA, November, 2004.
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View Large-Scale Semidefinite Programming via Saddle Point Mirror-Prox Algorithm