# Large-Scale Semidefinite Programming via Saddle Point Mirror-Prox Algorithm

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.