Adding (some) conic constraints.

[dnguyen227]

Adding some conic constraints that can be handled with BigM and Hull. Some things I found odd that maybe you can comment on or correct me.

1. Hull reformulation is standard throughout all cones, but cones in MOI inherit from AbstractVectorSet, so I can't just ask for any cone. Right now I'm stuck naming each type of cone rather than a generic MOI.Cone datatype.

2. BigM reformulation looks like it needs to be adapted per cone type, and right now I'm kind of having to reason out the correct direction based on the table provided in the paper. Snippet from the paper below.

Overall a good introduction to cones but I just can't get past these two things while I was trying to generalize the code.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 99.51%. Comparing base (48a1ac5) to head (3a83a41).

Additional details and impacted files

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  Coverage   99.51%   99.51%           
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  Files          17       17           
  Lines        2061     2075   +14     
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+ Hits         2051     2065   +14     
  Misses         10       10           

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[pulsipher]

Ya, we'll have to simply enumerate the conic sets. You could could make your own internal Union type though:

_ConicSets =Union{ExponentialCone, GeometricMeanCone, ...}

[pulsipher]

Thoughts @bernalde?

[bernalde]

Folks, this is exciting. I’ll do a more in depth review once you consider it useful, but one observation from my paper was the fact that the same cone appears in the BigM and HR reformulations, just involving the binary variables. If you already have access to the type of cone and how it was built, then you have everything to complete the recipe. Happy to talk more about this and provide code that we used (the repo in the paper should have all). Cheers!