jump-dev / jump-dev/MathOptInterface.jl

Add n-dimensional PowerCone

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Type: Set Request
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Julia
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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: https://github.com/jump-dev/MathOptInterface.jl/issues/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

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## Hypograph

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## Clarabel

Clarabel has native support for the radial with the restriction that $\sigma=1$ https://clarabel.org/stable/api_cone_types/

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## 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

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