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

By contributing to this software project, I have read the contribution guide and agree to the following terms and conditions for my contribution:

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 91.13924% with 28 lines in your changes missing coverage. Please review.
✅ Project coverage is 89.94%. Comparing base (6ab0106) to head (834ebd6).

Files with missing lines	Patch %	Lines
pyomo/contrib/piecewise/transform/factorable.py	91.11%	28 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #3821      +/-   ##
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+ Coverage   89.92%   89.94%   +0.01%     
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  Files         902      903       +1     
  Lines      106393   106709     +316     
==========================================
+ Hits        95679    95975     +296     
- Misses      10714    10734      +20     

Flag	Coverage Δ
builders	29.16% <20.88%> (-0.03%)	⬇️
default	86.25% <91.13%> (?)
expensive	35.59% <20.88%> (?)
linux	87.39% <91.13%> (-2.02%)	⬇️
linux_other	87.39% <91.13%> (+0.01%)	⬆️
oldsolvers	28.08% <20.88%> (-0.02%)	⬇️
osx	82.74% <91.13%> (+0.02%)	⬆️
win	85.83% <91.13%> (+0.02%)	⬆️
win_other	85.83% <91.13%> (+0.02%)	⬆️

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