[WIP] Propagate bounds when eliminating a linear, degree-2 constraint

[Robbybp]

Tighten bounds on the defining variable using bounds on the defined variable, if any, instead of adding inequalities.

[Robbybp]

Structural results

Model     & Method    & Var.   & Con.   & Elim. & NNZ/Con. & Lin. NZ/Con. & Hess. NNZ\\
\hline
DIST      & --        &  30368 &  30068 &     0 & 3.88 & 1.69 &  48032\\
DIST      & LD1       &  30300 &  30000 &    68 & 3.89 & 1.69 &  48000\\
DIST      & ECD2      &  29400 &  29100 &   968 & 3.62 & 1.68 &  47400\\
DIST      & LD2       &  29068 &  28768 &  1300 & 3.64 & 1.67 &  47400\\
DIST      & D2        &  19468 &  19168 & 10900 & 3.97 & 2.00 &  47100\\
DIST      & GR        &   9932 &   9632 & 20436 & 4.92 & 1.00 &  47700\\
DIST      & LM        &   9900 &   9600 & 20468 & 4.93 & 1.00 &  47700\\
\hline
MB        & --        &    870 &    869 &     0 & 3.09 & 1.39 &   1869\\
MB        & LD1       &    780 &    779 &    90 & 2.97 & 1.34 &   1451\\
MB        & ECD2      &    777 &    776 &    93 & 2.95 & 1.34 &   1366\\
MB        & LD2       &    592 &    591 &   278 & 3.24 & 1.28 &   1285\\
MB        & D2        &    491 &    490 &   379 & 3.38 & 1.34 &   1145\\
MB        & GR        &    300 &    299 &   570 & 5.24 & 0.80 &   1609\\
MB        & LM        &    167 &    166 &   703 & 9.23 & 0.02 &   1524\\
\hline
OPF       & --        &  61349 &  87120 &     0 & 3.06 & 2.27 &  75323\\
OPF       & LD1       &  58969 &  84740 &  2380 & 3.07 & 2.28 &  72981\\
OPF       & ECD2      &  55891 &  81662 &  5458 & 3.11 & 2.29 &  70249\\
OPF       & LD2       &  55567 &  81338 &  5782 & 3.11 & 2.29 &  70113\\
OPF       & D2        &  50650 &  86431 & 10699 & 2.93 & 1.78 &  70063\\
OPF       & GR        &  27152 & 120615 & 34197 & 3.21 & 2.42 & 149351\\
OPF       & LM        &  10396 & 138071 & 50953 & 3.93 & 0.24 &  80021\\
\hline
PIPE      & --        &  12293 &  12221 &     0 & 3.00 & 1.70 &  33506\\
PIPE      & LD1       &  10372 &  10300 &  1921 & 2.58 & 1.74 &  11155\\
PIPE      & ECD2      &   7281 &   7209 &  5012 & 2.81 & 1.74 &   9414\\
PIPE      & LD2       &   5252 &   5180 &  7041 & 3.13 & 1.90 &   9414\\
PIPE      & D2        &   4660 &   4588 &  7633 & 3.27 & 2.02 &   7708\\
PIPE      & GR        &   5492 &   6315 &  6801 & 3.52 & 0.97 &  16627\\
PIPE      & LM        &   1124 &   2186 & 11169 & 10.68 & 0.94 &  25393\\
\hline

The notable difference is that we now actually eliminate constraints with structure-preserving methods on the OPF model, and we eliminate noticeably more constraints in the pipeline model.

[Robbybp]

Convergence results

Distillation

     model     method  n-success  n-total  percent-success  ave-elim-time  ave-solve-time
0  distill    no-elim        103      121        85.123967       0.000021      196.634005
1  distill         d1        104      121        85.950413      83.219890      198.320097
2  distill    trivial        107      121        88.429752      99.527496      121.172014
3  distill  linear-d2        109      121        90.082645      97.635945       93.686453
4  distill         d2        121      121       100.000000     113.284353       89.352910
5  distill       ampl        119      121        98.347107      48.559953       79.228524
6  distill   matching        119      121        98.347107      85.264567       91.135404

Moving bed

       model     method  n-success  n-total  percent-success  ave-elim-time  ave-solve-time
0  mb-steady    no-elim         88      121        72.727273       0.000033        6.267466
1  mb-steady         d1         89      121        73.553719       5.377841        4.909835
2  mb-steady    trivial         89      121        73.553719       5.387387        5.035623
3  mb-steady  linear-d2         88      121        72.727273       6.289683        5.777489
4  mb-steady         d2         96      121        79.338843            NaN             NaN
5  mb-steady       ampl        105      121        86.776860       1.743644        1.374737
6  mb-steady   matching        101      121        83.471074       3.428107        1.176199

Pipeline

      model     method  n-success  n-total  percent-success  ave-elim-time  ave-solve-time
0  pipeline    no-elim         77      121        63.636364       0.000051      276.824916
1  pipeline         d1         99      121        81.818182      54.529603       29.298835
2  pipeline    trivial         98      121        80.991736      60.817973       17.694709
3  pipeline  linear-d2         99      121        81.818182      60.353903       16.281515
4  pipeline         d2         99      121        81.818182      66.426793       18.212334
5  pipeline       ampl         99      121        81.818182      16.108160       11.489716
6  pipeline   matching         99      121        81.818182            NaN             NaN

The only difference is that matching-pipeline does slightly better, while pipeline-trivial does slightly worse.

[Robbybp]

Solvetime results

Model     & Method    & $t_{\rm build}$ & $t_{\rm elim}$ & $t_{\rm init}$ & $t_{\rm solve}$ & Iter. & Func. & Jac. & Hess. & Other\\
\hline
DIST      & --        &   0.8 &    -- &   2.4 &   3.0 &  19 &   3 &   3 &   8 &  86\\
DIST      & LD1       &   0.8 &  32.7 &   2.2 &   3.0 &  19 &   3 &   3 &   8 &  86\\
DIST      & ECD2      &   0.8 &  37.5 &   2.4 &   1.6 &  17 &   5 &   5 &  12 &  78\\
DIST      & LD2       &   0.8 &  38.5 &   2.4 &   2.0 &  18 &   4 &   4 &  14 &  77\\
DIST      & D2        &   0.8 &  45.1 &   2.2 &   1.7 &  13 &   4 &   3 &  20 &  74\\
DIST      & GR        &   0.8 &  20.6 &   2.1 &   1.5 &  13 &   4 &   3 &  24 &  69\\
DIST      & LM        &   0.8 &  31.5 &   2.1 &   1.5 &  13 &   4 &   3 &  24 &  69\\
\hline
MB        & --        &   4.1 &    -- &   0.5 &   0.1 &   9 &  10 &   6 &  19 &  66\\
MB        & LD1       &   5.6 &   2.6 &   0.5 &   0.1 &   9 &  11 &   7 &  20 &  62\\
MB        & ECD2      &   5.7 &   2.7 &   0.5 &   0.1 &   9 &  10 &   8 &  18 &  64\\
MB        & LD2       &   5.8 &   3.1 &   0.4 &   0.1 &   9 &  11 &   7 &  22 &  60\\
MB        & D2        &   5.6 &   3.2 &   0.5 &   0.1 &  10 &  12 &   6 &  27 &  55\\
MB        & GR        &   3.8 &   1.0 &   0.5 &   0.1 &  10 &  12 &   5 &  30 &  53\\
MB        & LM        &   4.2 &   1.8 &   0.4 &   0.1 &  10 &  12 &   5 &  49 &  34\\
\hline
OPF       & --        &   2.9 &    -- &   3.9 &   9.9 &  61 &   4 &   4 &  10 &  81\\
OPF       & LD1       &   2.8 &  64.3 &   3.9 &   9.5 &  61 &   4 &   4 &   9 &  82\\
OPF       & ECD2      &   2.8 &  69.9 &   4.1 & 198.7 & 387 &   1 &   1 &   3 &  95\\
OPF       & LD2       &   2.8 &  76.5 &   4.6 & 3144.3 & 263 &   0 &   0 &   0 & 100\\
OPF       & D2        &   3.0 &  84.9 &   4.6 & 424.3 & 148 &   0 &   0 &   1 &  99\\
OPF       & GR        &   2.8 &  31.5 &   5.0 &  17.0 &  75 &   4 &   5 &  10 &  82\\
OPF       & LM        &   2.8 &  68.0 &   8.1 &  26.8 &  73 &   9 &  11 &  25 &  54\\
\hline
PIPE      & --        &   5.8 &    -- &   1.4 &   6.7 &  49 &   1 &   1 &   3 &  95\\
PIPE      & LD1       &   6.4 &  22.0 &   1.2 &   2.5 &  49 &   1 &   1 &   3 &  94\\
PIPE      & ECD2      &   6.1 &  24.0 &   1.1 &   2.1 &  51 &   2 &   1 &   5 &  92\\
PIPE      & LD2       &   6.0 &  24.8 &   1.1 &   1.1 &  34 &   2 &   2 &   7 &  89\\
PIPE      & D2        &   6.0 &  26.5 &   1.2 &   0.9 &  34 &   2 &   2 &   7 &  88\\
PIPE      & GR        &   6.0 &   7.5 &   1.3 &   1.4 &  30 &   3 &   2 &   9 &  87\\
PIPE      & LM        &   5.8 &  50.0 &   1.9 &   3.1 &  35 &   2 &   4 &  76 &  18\\
\hline

Something weird is still happening with OPF. I'll run this with tee=True to see what's going on, but if it isn't anything we can fix, we probably have to shelf this idea.