Description
@lkapelevich and @HFriberg have been emailing me about the upcoming CBF v4, https://cblib.zib.de/doc/format4.pdf, which proposes to add an n-dimensional PowerCone.
We've talked about this somewhat before: #977
There are two proposed variants (plus their dual cones).
I have no strong feelings on which ones (if any) we should adopt. But I'd like to somewhat reign in having a litany of very similar cones.
Radial

Hypograph

Clarabel
Clarabel has native support for the radial with the restriction that

Hypatia
Hypatia has both https://jump.dev/Hypatia.jl/stable/api/cones/#Hypatia.Cones.GeneralizedPower and https://jump.dev/Hypatia.jl/stable/api/cones/#Hypatia.Cones.HypoPowerMean
Mosek
Mosek has support for radial: https://docs.mosek.com/latest/capi/alphabetic-functionalities.html#mosek.task.appendprimalpowerconedomain
