Ease addition of matrix cones

[blegat]

The PSDCone allows to easily add MOI.PositiveSemidefiniteConeTriangle and MOI.PositiveSemidefiniteConeSquare.
There are several other matrix cones, that should work exactly like PSDCone for consistency:

• SemidefiniteInterval, SemidefiniteGreaterThan and SemidefiniteLessThan that create MOI....Triangle and MOI....Square, see Matrix bounds MathOptInterface.jl#942
• EigenvalueInterval, EigenvalueGreaterThan and EigenvalueLessThan that create MOI....Triangle and MOI....Square, see Matrix bounds MathOptInterface.jl#942
• SumOfSquares.DDCone that create SumOfSquares.DiagonalyDominantConeTriangle and SumOfSquares.DiagonalyDominantConeSquare
• SumOfSquares.SDDCone that create SumOfSquares.ScaledDiagonalyDominantConeTriangle and SumOfSquares.ScaledDiagonalyDominantConeSquare

To allow reusing the code for PSDCone between these different sets we can create a AbstractSymmetricMatrixCone set and the function triangle_vectorized_cone and square_vectorized_cone and then all the code should work for any AbstractSymmetricMatrixCone.

Requires jump-dev/MathOptInterface.jl#942

[odow]

@blegat: We haven't made any progress on this. I see what we closed #942, so I'm not sure what Requires #942 is for. Can this be closed? We seem to be getting on okay without it.

[blegat]

I'll take a look whilr adding affine hermitian constraints. It would still be helpful

[odow]

Bump. Is there anything to do here?

[blegat]

Yes, I still need to get at it

[odow]

Can you point me in the right direction? I still don't really understand what you're after.

[blegat]

I'm going to take a look

[odow]

Can you be a little more explicit in what you want here? For example, links to the bits in other packages that would be de-duplicated?

[blegat]

These are the cones: https://github.com/jump-dev/SumOfSquares.jl/blob/8476c96d0fc182377a3a585222714061925092ab/src/diagonally_dominant.jl
I haved made it possible to use them from JuMP as it would be duplicating the code

[odow]

So you want a fallback for any MOI.AbstractSymmetricMatrixSetTriangle?

[blegat]

Yes