Making Hypatia more extensible

[rcywongaa]

First of all, thanks for the amazing library!

This is a followup to #839

My understanding is that one of the main features of Hypatia is its ability to model user-specified cones via the generic cone interface. However, at the moment, using a custom cone requires editing and/or duplicating multiple files/functions: src/MathOptInterface/wrapper.jl and src/MathOptInterface/cones.jl which isn't really relevant to the cone.

I'm wondering if we could make it easier to make Hypatia work with custom cones.

I've played around a bit and found that we could make things easier by merging the Cone and MOI.AbstractVectorSet versions of cones together thus only having one Cone interface that also works with MOI.

See #848 for a draft of the minimal changes (not including cleaning up examples, etc.)

This allows users allows to just implement the Cone interface and have stuff work out of the box (it seems).

I understand this is perhaps a substantial change and lots of examples/benchmarks may need to be cleaned up after this change so I'd like to hear your feedback before doing anything else.

[araujoms]

That would be awesome! The current approach requires not only a lot of boilerplate, but also makes it impossible to load two independent extensions simultaneously.

[lkapelevich]

Thanks @rcywongaa for the summary. I don't see a broad reason for Cone to inherit from MOI :-/.

For the redefinining MOI.* annoyance, maybe there's a workaround with making the HypatiaCones type like
HypatiaCones <: MOI.AbstractVectorSet and the Hypatia MOI cones simply inherit from HypatiaCones? I haven't thought about it.

I'm not the best person here to make suggestions for this, sorry!

[rcywongaa]

My understanding is subtyping MOI is necessary for Cone to work with JuMP which seems to be the recommended way.

If I understand correctly, my proposed change is exactly to change the current Cone to your proposed HypatiaCones which subtypes <: MOI.AbstractVectorSet

[lkapelevich]

The cones and other modules except where the wrapper is, are independent from MOI. Someone could write a separate wrapper for a different modeling interface :).

I said HypatiaCones because it's already defined in the wrapper.

[rcywongaa]

Ok, I understand the concern now.

I've turned HypatiaCones into an abstract type that subtypes MOI.AbstractVectorSet and renamed it MOICone. This allows us to keep the original Cone interface unchanged and keeps the MOI specific stuff within MathOptInterface/

To further reduce boilerplate, I've also added a MOIWrapper type that directly converts a Hypatia.Cones:Cone into a JuMP compatible cone without having to define a custom MOICone

Please see #850