Discuss extended formulations in docs #396
Merged
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I'm not 100% sure this is the best place for it, but I wanted it somewhere people would see it fairly quickly, because I think it makes it more clear what exactly Convex.jl is doing and why DCP warnings are important. As I've worked on #393, I've realized the obvious fact that the central/only thing Convex.jl does is automatic application of extended formulations, and I didn't find that to be completely clear from the docs, so I wanted to write about it somewhere central.
The other reason for adding this is to make the issue with non-DCP problems more clear. I actually haven't seen too many issues where people are solving non-DCP problems and getting confused by the fact that the results are wrong, but I do think it can be confusing why that happens. For example, I thought for awhile that the main problem was it was a nonconvex problem and you are finding a local solution instead; really the issue is you are solving a completely different problem since the reformulation was invalid, and I hope the
abs
example makes that clear.