I'm now solving an LP that has a few coupling rows (as in Dantzig-Wolfe decomposition) and a few coupling columns (as in Benders decomposition) simultaneously; other rows and columns are block-angular. Is there an algorithm that decomposes such LP? Thank you very much!



Combining Dantzig-Wolfe and Benders decomposition
You could apply Benders as the main algorithm and use Dantzig-Wolfe for the subproblem. Alternatively, you could apply Dantzig-Wolfe as the main algorithm and use Benders for the subproblem. For LP, Benders and Dantzig-Wolfe are equivalent if you take duals, so you could also either apply Benders as the main algorithm and Benders for the dual of the subproblem or Dantzig-Wolfe as the main algorithm and Dantzig-Wolfe for the dual of the subproblem.


