Piecewise Linear transformations: Logarithmic and nested inner GDP representation

[sadavis1]

Fixes # .

Summary/Motivation:

We want to add piecewise-linear to GDP and to MIP transformations from Vielma 2010 so they can be used in Bashar's PWL representations paper.

Changes proposed in this PR:

• Add disaggregated_logarithmic transformation for PW linear, direct to mip as in Vielma
• Add "nested_inner_repn" transformation, which should be a path to GDP-ification of Vielma's log transformations by identifying some variables, once some changes are made to gdp transformations to support it. Also, this transformation is somewhat interesting in its own right, because it is often faster than the inner representation despite not actually having the logarithmic variable count.
• Rename class PiecewiseLinearToGDP to PiecewiseLinearTransformationBase, since it isn't GDP-specific and I'm using it for a MIP.

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[bernalde]

Really cool PR!
Just saw a couple of typos! The interesting part would be the benchmarking once this is merged

[sadavis1]

Fixed typos and some other minor issues.

[emma58]

This is looking quite good!

[sadavis1]

This should be ready now. The linux/3.12 test failure seems to be spurious.

[emma58]

A few comments, but this is looking quite good! My only concern is if there are tests that are common to multiple transformations, we should centralize them so that if things change in the future we only have to make changes in one place.

[emma58]

For this and the others that are identical to the inner representation GDP, can we put these methods in the common_tests and just check them in both?

[sadavis1]

It wouldn't really be appropriate for common_tests, since that file is also used for other transformations that are not inner representation-related. We could do this by moving the methods into a superclass between unittest.TestCase and the transformation test class, but I feel like that's unnecessarily complex to only house two duplicated methods. Well, we could start moving the test method boilerplate into the superclass too, but then it becomes inconsistent with the other transformations that have all their test methods duplicated.

[emma58]

Maybe lets not convolute the class structure any more--I agree that that's not worth it, but could we move the methods themselves into functions in common_tests (or make a short common_inner_repn_tests script if you prefer), and just make this method call that function? I do this in GDP a lot: my convention is to name the function check_whatever, have its first argument be the test class (self) and then in the test_whatever method, I just call check_whatever. Sorry to be picky, but maintaining tests in code that could potentially change a lot is really hard, and I think having it be very clear to future us what we expect to be common will be nice. :)

[sadavis1]

That works. I've moved the methods to a common_inner_repn_tests file.

[sadavis1]

Oh... oops. I seem to have done something strange with git. One minute..

[emma58]

Looks good!

[codecov]

Codecov Report

Attention: Patch coverage is 96.05263% with 6 lines in your changes are missing coverage. Please review.

Project coverage is 86.55%. Comparing base (69082ac) to head (e954043).

Files	Patch %	Lines
...o/contrib/piecewise/transform/nested_inner_repn.py	93.67%	5 Missing ⚠️
...b/piecewise/transform/disaggregated_logarithmic.py	98.36%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #3036      +/-   ##
==========================================
- Coverage   88.39%   86.55%   -1.85%     
==========================================
  Files         847      849       +2     
  Lines       95263    95405     +142     
==========================================
- Hits        84212    82582    -1630     
- Misses      11051    12823    +1772     

Flag	Coverage Δ
linux	?
osx	?
other	83.83% <96.05%> (-2.70%)	⬇️
win	83.83% <96.05%> (+<0.01%)	⬆️

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[jsiirola]

I think this looks good. I went ahead and changed the one thing that was bothering me (converting int to binary vectors without going through strings)

The requested changes have been made