Make Hessian sparsity detection work with SCT (prototype)

[gdalle]

This is just an example showing how to replace certain dense matrices with sparse ones to turn accidental zeros into structural zeros. This is enough to make the MWE of #193 work with SCT, but I haven't run wider tests, and I don't think you should merge this PR without a deeper reflection on structural sparsity handling

[franckgaga]

@gdalle
I would not merge this PR explicitly but another PR with similar ideas but implemented differently. Mainly: be more efficient with decision variables $\mathbf{Z}$ to input increments $\mathbf{\Delta }\mathbf{U}$ and input $\mathbf{U}$ conversions, but without explicitly using sparse-matrix.

Are you are of way to incorporate your ideas in a new pull request and explicitly mark you as a contributor ? The idea comes from you, so I would like you to appear as a contributor on the github page! Maybe just a dummy commit in the other PR?

[gdalle]

Thanks for being so thoughtful about contributors!
Perhaps the easiest way would be for you to take this PR branch, add a second commit which undoes my first commit, and then be on your merry way to add more stuff?

[franckgaga]

Yes great idea, I'll do this.

edit: maybe not. Many commits that I wrote in JuliaControl:hessian_objective_debug branch are simply thrown away (since it is not possible to implement this feature with JuMP right now). So I would need to revert your commits and many of my commits before that. I think I'll use cherry picking.

[franckgaga]

Closing in favor of #202 that uses cherry-picking

[gdalle]

Just so you know, we're still planning on merging adrhill/SparseConnectivityTracer.jl#243, it's just a bit more complicated than we thought because it interferes with array-level overloads (essentially if we regard matrices or vectors of constants as black boxes in SCT, then we can't cherry-pick the non-zero coefficients)