[Nonlinear] add support for univariate sign

[odow]

Closes #2448

I don't know about this one. We might be better off documenting people to write a signpower function at the JuMP level because this still has the problem that sign(x) * abs(x)^p is not defined when x=0 and p < 1.

Thoughts @ccoffrin?

[ccoffrin]

My hot take.

There may be other uses of sign we cannot anticipate, which don't have such an obvious work around.
If the following conditions are met,

1. Adding support for a new function does not add a major burden (e.g., in maintenance)
2. It is a very common built-in Julia function (ideally also part of C standard functions)
3. there have been multiple request for support (i.e., users want it)

Then I think it is good to add support for it.

I hear your point that this will likely lead to a bunch of non-ideal modeling choices by non-experts. However, that issue is not limited to this specific new feature. I don't think there is an easy work around for helping typical users model better. Current state of the art is basically to get a PhD in NLP to understand how to write better models.

[odow]

sign meets your criteria for 1, 2, and 3.

It's probably the currently unsupported operator that I see most often.

And we already support min, max, ifelse, and abs, so non-differentiatbility isn't an argument against adding.

@mlubin should weigh in before we decide to merge.

[blegat]

I agree with @ccoffrin 's comment