Add the DCP of Qiu et al

[klamike]

https://arxiv.org/pdf/2310.02969

Steps 1-5 requires a custom decomposition/projection, step 6 is the completion.

Should also explore automating the detection of the Lemma 2 for use in other problems

Eventually do the SDP version as well https://arxiv.org/pdf/2502.06978

cc @ivanightingale

[ivanightingale]

This procedure was very specific to SOC-OPF. Do you want to do it for general convex problems? If so, this paper did propose several recovery steps that are not Euclidean projections (which may be what you meant by custom decomposition/projection), so they can bring something new to this repo.

[klamike]

The main idea of this issue is that this repo should have somewhere a tutorial on how to use it to implement your method -- specific to SOCOPF. That tutorial can serve a dual purpose as also explaining how to use custom projections/why that is a useful feature.

Secondary goal is to make detection functions corresponding to each of your lemmas that detect if they can be applied (to an arbitrary problem).