Use projected NLPs for the inner problem solves in ExternalPyomoModel

[Robbybp]

Summary/Motivation:

There is a significant performance improvement for some problems if we create ProjectedNLPs that we solve repeatedly with CyIpopt, rather than solve Pyomo blocks with Ipopt, for the inner problems in the implicit function formulation.

Changes proposed in this PR:

• Add the data structures necessary to repeatedly solve a sequence of square problems as PyomoNLPs, where variables are updated before each solve
• Change the default behavior of ExternalPyomoModel to solve ProjectedNLPs with CyIpopt, and only use Ipopt (or another Pyomo solver) if specified, or if CyIpopt is unavailable.

A comparison comparison on a chemical looping steady state optimization problem:

• Current main:
  
• This branch
  

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[codecov]

Codecov Report

Merging #2283 (34670ae) into main (3e6a869) will decrease coverage by 0.08%.
The diff coverage is 100.00%.

@@            Coverage Diff             @@
##             main    #2283      +/-   ##
==========================================
- Coverage   85.29%   85.21%   -0.09%     
==========================================
  Files         611      616       +5     
  Lines       76006    77925    +1919     
==========================================
+ Hits        64833    66407    +1574     
- Misses      11173    11518     +345     

Flag	Coverage Δ
linux	82.70% <100.00%> (+<0.01%)	⬆️
osx	72.91% <6.66%> (+<0.01%)	⬆️
other	82.66% <100.00%> (+<0.01%)	⬆️
win	79.79% <100.00%> (+0.01%)	⬆️

Flags with carried forward coverage won't be shown. Click here to find out more.

Impacted Files	Coverage Δ
...ontrib/pynumero/interfaces/external_pyomo_model.py	99.27% <100.00%> (+0.13%)	⬆️
...o/contrib/interior_point/linalg/mumps_interface.py	43.95% <0.00%> (-31.05%)	⬇️
pyomo/contrib/pynumero/linalg/mumps_interface.py	74.69% <0.00%> (-14.67%)	⬇️
pyomo/contrib/pynumero/linalg/ma27.py	84.48% <0.00%> (-14.47%)	⬇️
...mo/contrib/interior_point/linalg/ma27_interface.py	72.81% <0.00%> (-5.31%)	⬇️
pyomo/contrib/appsi/solvers/cplex.py	78.83% <0.00%> (-4.51%)	⬇️
...erior_point/linalg/base_linear_solver_interface.py	77.77% <0.00%> (-1.39%)	⬇️
pyomo/core/base/alias.py	0.00% <0.00%> (ø)
pyomo/contrib/mindtpy/MindtPy.py	100.00% <0.00%> (ø)
pyomo/contrib/pynumero/linalg/ma27_interface.py	20.48% <0.00%> (ø)
... and 18 more

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[jsiirola]

elif to avoid the extra indentation?

[Robbybp]

See comment below. I think I want to have this extra if statement so that the increment of vector_scc_idx happens regardless of whether we're using CyIpopt.

[jsiirola]

I think this is technically correct as written, but it would be clearer if it was done inside the if self._use_cyipopt block.

[Robbybp]

I think I like having this outside the if self._use_cyipopt tree, as otherwise, in the case where we use a regular Pyomo solver, vector_scc_idx will always be zero, even though we may not be at the zeroth "vector-valued" SCC. Having this information may be useful, e.g. for debugging, even if it's not strictly necessary for the algorithm.