Implement different examples to test decomposition algorithms

[frapac]

I think it would be interesting to implement a bank of examples to test the different decomposition algorithms. Ideally, the examples would be generated such that

• they represent some kind of real-world problem ;
• we can parameterize their size (ie the number of blocks) ;
• we can parameterize the couplings between the subproblems (that last point is more difficult though).

For now, I have the following instances in mind:

• The single commodity network flow introduced in Boyd's note
• The LQR problem
• the Network Utility Maximization and the Linear Network Flow problems introduced in this paper (randomly generated, graph structure)
• stochastic optimization instances (as those already implemented in StructJuMP.jl)
• the decentralized examples implemented in ALADIN

Let me know if you have other examples in mind.

[grishabh147]

We can also implement some machine learning problems as almost all of them have a block structure. I would also like to test different algorithms on the inverse convex optimization problem (do not have a good reference yet).

[AnirudhSubramanyam]

I completely agree about having the ability to parameterize the size of individual blocks and the number of blocks. But shouldn't this be an issue in the BlockNLPAlgorithms.jl package?

[frapac]

But shouldn't this be an issue in the BlockNLPAlgorithms.jl package?

you are totally right! I can transfer the issue as soon as BlockNLPAlgorithms.jl is created!