Parallel subgradient algorithm with block dual decomposition for large-scale optimization

•Trade-off between minimizing the number of dualized constraints and detecting a structure amenable to parallel optimization.•Our approach accelerates the convergence of the distributed sub-gradient method when compared to the dual decomposition.•Denser constraint matrix leads to a higher number of dualized constraints and more iterations for convergence.•It is crucial to employ prior knowledge about the structure of the problem when solving large scale optimization problems.