Separate Linear Terms in Nonlinear to Piecewise Linear Transformation

[michaelbynum]

Summary/Motivation:

This PR modifies the contrib.piecewise.nonlinear_to_pwl transformation so that linear parts of a constraint always get separated from the nonlinear parts, even if additively_decompose is False. The idea is that

y >= exp(x) + x**3

should become

y >= PWL(exp(x) + x**3)

and not

0 >= PWL(exp(x) + x**3 - y)

Legal Acknowledgement

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1. I agree my contributions are submitted under the BSD license.
2. I represent I am authorized to make the contributions and grant the license. If my employer has rights to intellectual property that includes these contributions, I represent that I have received permission to make contributions and grant the required license on behalf of that employer.

[codecov]

Codecov Report

❌ Patch coverage is 89.65517% with 3 lines in your changes missing coverage. Please review.
✅ Project coverage is 89.44%. Comparing base (e0fcc81) to head (cff61ab).

Files with missing lines	Patch %	Lines
...mo/contrib/piecewise/transform/nonlinear_to_pwl.py	89.65%	3 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #3814      +/-   ##
==========================================
- Coverage   89.45%   89.44%   -0.01%     
==========================================
  Files         905      905              
  Lines      105467   105492      +25     
==========================================
+ Hits        94341    94361      +20     
- Misses      11126    11131       +5     

Flag	Coverage Δ
builders	29.13% <10.34%> (-0.02%)	⬇️
default	86.07% <89.65%> (?)
expensive	35.76% <10.34%> (?)
linux	86.76% <89.65%> (-2.45%)	⬇️
linux_other	86.76% <89.65%> (-0.01%)	⬇️
osx	82.92% <89.65%> (-0.01%)	⬇️
win	85.00% <89.65%> (-0.01%)	⬇️
win_other	85.00% <89.65%> (-0.01%)	⬇️

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[emma58]

I think this makes sense. If you could put in a comment with the example you put in the PR description for why _separate_linear_parts is necessary, I think that would be helpful for future us. My guess is this is not currently the fastest thing we could possibly do, but for now, I'm not so concerned with that. @jsiirola, @sadavis1, @bammari, this might be worth glancing at if you have a minute.

[emma58]

Does separating these two cases matter? I mean, obviously you make a different expression tree, but do we need it?

[michaelbynum]

I don't think it matters to me.

[michaelbynum]

I'm going to leave this just for consistency with QuadraticRepn.

[emma58]

@jsiirola, can this happen? I have something in the back of my mind telling me multiplier is sure to be 1 at this point?

[michaelbynum]

I just copied the to_expression code from the QuadraticRepn class and modified it slightly...

[michaelbynum]

which is to say that I have no idea. I'll take a look, though.

[michaelbynum]

Oh, I can't read. This question was for @jsiirola. My bad.

[michaelbynum]

Okay, if this does make some sense, I'll clean it up a bit.

[michaelbynum]

Okay, assuming tests pass, this should be good to go.

[emma58]

This looks good to me. I still have the multiplier question, if you can check that when you look, @jsiirola