Modify PyROS DR Order Efficiency

[shermanjasonaf]

Summary/Motivation:

The PyROS solver currently institutes, as an algorithmic efficiency, the following heuristic for the polynomial decision rule (DR) coefficients of a problem with $n_q$ uncertain parameters:

• In iteration 0: fix coefficients of all nonstatic DR terms to 0
• In iterations 1, 2, ..., $n_q$: fix coefficients of only the quadratic DR terms to 0
• In iterations $n_q + 1, n_q + 2, \dots$: unfix all coefficients

In light of #3533, we have found that:

• When there are first-stage equality constraints involving the DR variables, instituting the efficiency above may cause PyROS to return suboptimal solutions or terminate prematurely with a(n inaccurate) robust infeasibility status. Such constraints may arise from reformulation (through, for example, coefficient matching) of second-stage equalities that are independent of the state variables
• Since, as of Add PyROS Uncertain Parameter Reduction #3503, DR variables are not declared for polynomial terms involving only uncertain parameters that are constrained to unique values (i.e., effectively certain parameters), all coefficients should be unfixed by iteration $\tilde{n}_{q} + 1$, rather than $n_q + 1$, where $\tilde{n}_q$ is the number of effective uncertain parameters, such that $\tilde{n}_q \leq n_q$.

Thus, in this PR, the heuristic is modified to the following:

• If there are DR variable-dependent first-stage equalities, then unfix all DR coefficients in all iterations
• Else, fix all nonstatic term coefficients in iteration 0, fix only the quadratic term coefficients in iteration 1, 2, ..., $\tilde{n}_q$, and unfix all coefficients in all subsequent iterations

Changes proposed in this PR:

• Distinguish between DR variable-dependent and DR variable-independent equality constraints in the first-stage block of the preprocessed working model
• Modify the polynomial DR order heuristic
• Add tests based on problems that are sensitive to the DR order heuristic

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

All modified and coverable lines are covered by tests ✅

Project coverage is 88.73%. Comparing base (0b58294) to head (bb610f5).
Report is 46 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #3562      +/-   ##
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- Coverage   88.73%   88.73%   -0.01%     
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  Files         890      890              
  Lines      102194   102208      +14     
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+ Hits        90682    90694      +12     
- Misses      11512    11514       +2     

Flag	Coverage Δ
builders	26.61% <4.34%> (+<0.01%)	⬆️
default	84.85% <100.00%> (?)
expensive	34.00% <4.34%> (?)
linux	86.24% <100.00%> (-2.24%)	⬇️
linux_other	86.24% <100.00%> (+<0.01%)	⬆️
osx	76.19% <100.00%> (+<0.01%)	⬆️
win	84.74% <100.00%> (-0.01%)	⬇️
win_other	84.74% <100.00%> (-0.01%)	⬇️

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