Exotic2Common: avoid stack atoms in PowConeND to PowCone3D reduction

[rileyjmurray]

Following PR #1211, cvxpy supports 3D and ND power cone constraints. The main way for doing this is the (Exotic2Common) that maps an ND power cone to a collection of (N-2) 3D power cones. As-implemented, this reduction has two downsides:

1. The canonicalization involves use of hstack atoms and other high-level affine transformations. This use of high-level atoms will likely be more expensive to canonicalize in cvxcore compared to if we built suitable sparse matrices directly.
2. The PowConeND class currently does not have dual variable support. (Resolved in 2023 by PR Dual variables for PowConeND #2241.)

We'd welcome contributions handling either of these issues.

We'd welcome contributions for handling the remaining issue.

[rileyjmurray]

For (2), see this writeup on how dual variables for the 3D power cone lift of the ND power cone can be propogated back as dual variables for the original ND power cone.

[pat749]

hi @rileyjmurray currently i am working on it and i am also reading arxiv research paper which you have given ,but i have a simple doubt should hamza fawzi paper also have to implemented using cvxpy and also any suggestion for this task? thanks

[pat749]

and also any discourse group where i can join

[rileyjmurray]

Hi @pat749, nice to hear you're taking this on! Hamza Fawzi's papers are not needed for this task. We can have discussions here, on Discord, or on GitHub Discussions.

[pat749]

ok thanks

[rileyjmurray]

@pat749 have you worked on this? If so, can you please push your code to a public repository so I can see where you're at?

[pat749]

yes i have worked on it just some work remaining ,currently i am busy due to proposal writting for gsoc
and also college exam i will try to complete it by 17-18 april. i have some doubt about this can i get some more references about ND power cone?

[goulart-paul]

We have added native support for ND power cones in Clarabel v0.6.0, including updates to the python wrapper.

Very basic example here. Better documentation than that still to come.