Factorable Programming for PWL Approximations

[michaelbynum]

Summary/Motivation:

The purpose of this module/transformation is to convert any nonlinear model
to the following form:

min/max e(x_i)*f(x_j) + b^T*x
s.t.
        g_j(x_i)*h_j(x_k) + a_j^T*x >/</== 0
        g_j(x_i)/h_j(x_k) + a_j^T*x >/</== 0
        g_j(x_i)**h_j(x_k) + a_j^T*x >/</== 0

By doing so, each nonlinear function is only a function of one or two variables.
If this transformation is used prior to the nonlinear_to_pwl transformation,
it can, in some cases, significantly reduce the complexity of the PWL approximation.

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 91.49660% with 25 lines in your changes missing coverage. Please review.
✅ Project coverage is 89.68%. Comparing base (bdb22dd) to head (ce55a10).

Files with missing lines	Patch %	Lines
pyomo/contrib/piecewise/transform/factorable.py	91.46%	25 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #3821      +/-   ##
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+ Coverage   89.67%   89.68%   +0.01%     
==========================================
  Files         908      909       +1     
  Lines      106735   107029     +294     
==========================================
+ Hits        95717    95994     +277     
- Misses      11018    11035      +17     

Flag	Coverage Δ
builders	29.05% <18.02%> (-0.02%)	⬇️
default	85.98% <91.49%> (?)
expensive	35.46% <18.02%> (?)
linux	87.15% <91.49%> (-2.02%)	⬇️
linux_other	87.15% <91.49%> (+0.01%)	⬆️
oldsolvers	27.97% <18.02%> (-0.03%)	⬇️
osx	82.07% <91.49%> (+0.02%)	⬆️
win	85.58% <91.49%> (+0.02%)	⬆️
win_other	85.58% <91.49%> (+0.02%)	⬆️

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