Presolve isn't identifying redundant constraints in QCPs
Ongoing
I am comparing the results of two QCPs, a smaller one and a larger one. The only difference between these two QCPs is the inclusion of one linear constraint. By construction, this linear constraint is redundant -- it is the sum of two already-existing constraints. Hence, the objectives of the smaller and larger QCPs should be the same. However, I am getting different objectives.
The log output of smaller QCP displays the following information (see below for full log output):
140 rows, 50 columns, 616 nonzeros
1 quadratic constraint
Presolve removed 114 rows and 32 columns
Presolved: 38 rows, 44 columns, 208 nonzeros
Presolved model has 1 second-order cone constraint
Meanwhile, the log output of the larger QCP displays the following information:
141 rows, 50 columns, 138 nonzeros
1 quadratic constraint
Presolve removed 114 rows and 32 columns
Presolved: 39 rows, 44 columns, 208 nonzeros
Presolved model has 1 second-order cone constraint
The presolved model should be the same if Gurobi recognizes that the larger model has a redundant constraint. However, the log file shows that the resolved models are indeed different.
To debug this further, I followed the steps suggested in this post, which describes how presolve works. I saved the model following the presolve step for both the small and the large model. It turns out that the redundant constraint in the larger model survives the presolve stage. For more details, here is an excerpt of the LP file for the larger model:
R100: C0 + C1 + 2 C5 + 2 C6 - C10 - C11 <= 0
R105: C1 + 2 C6 - C11 <= 0
R140: C0 + 2 C1 + 2 C5 + 4 C6 - C10 - 2 C11 <= 0
Observe that adding R100 and R105 yields R140, i.e., satisfying R100 and R105 will automatically satisfy R140.
Why doesn't Gurobi remove this redundant constraint during the presolve?
---
My further attempts at debugging this issue include the following:
- I set the \(\texttt{Presolve}\) parameter to 2 (i.e., aggressive), but nothing changed from the default value.
- I removed the quadratic constraint. Without the quadratic constraint, all the rows and columns were removed in the presolve step for both the smaller and larger QCP.
---
In case it helps, I am pasting the contents of four files below in the following order:
- log of the smaller model
- lp file after presolving the smaller model
- log of the larger model
- lp file after presolving the larger model
1. log of the smaller model
Gurobi 9.1.2 (mac64, R) logging started Tue Sep 7 14:59:33 2021
Academic license - for non-commercial use only - expires 2022-08-03
Gurobi Optimizer version 9.1.2 build v9.1.2rc0 (mac64)
Thread count: 4 physical cores, 8 logical processors, using up to 8 threads
Optimize a model with 140 rows, 50 columns and 616 nonzeros
Model fingerprint: 0xd0153e79
Model has 1 quadratic constraint
Coefficient statistics:
Matrix range [1e+00, 4e+00]
QMatrix range [5e-02, 2e+00]
QLMatrix range [3e-01, 4e+00]
Objective range [1e+00, 1e+00]
Bounds range [0e+00, 0e+00]
RHS range [2e+00, 5e+00]
QRHS range [3e+00, 3e+00]
Presolve removed 56 rows and 0 columns
Presolve time: 0.01s
Presolved: 96 rows, 100 columns, 496 nonzeros
Presolved model has 1 second-order cone constraint
Ordering time: 0.00s
Barrier statistics:
AA' NZ : 1.437e+03
Factor NZ : 1.637e+03
Factor Ops : 3.183e+04 (less than 1 second per iteration)
Threads : 1
Objective Residual
Iter Primal Dual Primal Dual Compl Time
0 -1.34588457e+01 -1.10314866e+03 1.35e+03 7.02e-01 2.59e+02 0s
1 -7.71206509e+01 -3.09513309e+02 3.44e+02 1.28e-02 5.86e+01 0s
2 -5.41183774e+00 -2.36840986e+02 1.25e+01 1.41e-08 3.46e+00 0s
3 -4.10131245e+00 -7.34495651e+01 3.08e+00 6.62e-10 7.59e-01 0s
4 -3.16484827e+00 -2.40601971e+01 1.22e+00 3.55e-11 2.06e-01 0s
5 -5.72989330e-01 -1.04443377e+01 4.92e-01 7.92e-12 8.44e-02 0s
6 -1.20634176e+00 -7.39120102e+00 3.14e-01 4.72e-12 5.17e-02 0s
7 -6.68470197e-01 -2.68815990e+00 1.67e-01 1.69e-12 2.04e-02 0s
8 1.99295324e-02 -1.56702729e+00 1.04e-01 1.13e-12 1.56e-02 0s
9 8.64507602e-01 2.39319083e-02 3.83e-02 4.33e-13 8.55e-03 0s
10 1.40179748e+00 1.48791136e+00 1.35e-02 6.80e-14 1.90e-03 0s
11 1.57800635e+00 1.75305134e+00 5.16e-03 1.14e-13 2.02e-04 0s
12 1.69415984e+00 1.81330094e+00 3.20e-03 8.53e-13 1.09e-04 0s
13 1.72662543e+00 1.84781250e+00 2.63e-03 1.08e-12 2.84e-05 0s
14 1.76586927e+00 1.86053670e+00 1.92e-03 6.88e-12 3.74e-05 0s
15 1.78993953e+00 1.87265766e+00 1.51e-03 4.66e-12 2.43e-05 0s
16 1.79966744e+00 1.88419798e+00 1.38e-03 7.05e-12 1.87e-05 0s
17 1.83115946e+00 1.87376837e+00 9.00e-04 5.42e-11 9.67e-05 0s
18 1.82318086e+00 1.87796242e+00 6.95e-04 4.04e-11 7.09e-05 0s
19 1.87044321e+00 1.87967681e+00 4.39e-04 8.79e-11 3.39e-04 0s
20 1.90670779e+00 1.89023115e+00 2.44e-04 6.62e-11 4.53e-04 0s
21 1.93797527e+00 1.95455139e+00 4.56e-05 4.09e-12 1.39e-05 0s
22 1.94552130e+00 1.95503579e+00 2.95e-05 8.94e-10 1.29e-05 0s
23 1.94840146e+00 1.95559787e+00 5.03e-06 2.11e-09 1.01e-07 0s
24 1.94886845e+00 1.95560097e+00 4.56e-06 3.23e-07 1.10e-09 0s
Barrier solved model in 24 iterations and 0.01 seconds
Optimal objective 1.94886845e+00
2. lp file after presolving the smaller model
\ Model R_pre
\ LP format - for model browsing. Use MPS format to capture full model detail.
Minimize
- C12 + C37
Subject To
R2: C2 + 2 C7 - C12 + C94 = 2
R3: C2 + C3 + 2 C7 + 2 C8 - C12 - C13 + C97 = 2
R7: C7 - C12 + C82 = 2
R8: C7 + C8 - C12 - C13 + C91 = 2
R9: C7 + 2 C8 + C9 - C12 - 2 C13 - C14 + C95 = 2
R10: C10 + 2 C11 - C12 + C85 = 2
R11: C11 - C12 <= 2
R15: C10 + 2 C11 - C12 + C15 + 2 C16 - C17 + C92 = 2
R16: C11 - C12 + C16 - C17 + C87 = 2
R20: C10 + 2 C11 - C12 + 2 C15 + 4 C16 - 2 C17 + C20 + 2 C21 - C22 = 2
R21: C11 - C12 + 2 C16 - 2 C17 + C21 - C22 + C89 = 2
R25: - C25 - 2 C26 + C27 - 2 C30 - 4 C31 + 2 C32 + C35 + 2 C36 - C37 = 2
R27: C27 + 2 C32 - C37 + C67 = 2
R28: C27 + C28 + 2 C32 + 2 C33 - C37 - C38 + C80 = 2
R32: C32 - C37 + C63 = 2
R33: C32 + C33 - C37 - C38 + C70 = 2
R34: C32 + 2 C33 + C34 - C37 - 2 C38 - C39 + C77 = 2
R35: C35 + 2 C36 - C37 + C66 = 2
R36: C36 - C37 <= 2
R40: C35 + 2 C36 - C37 + C40 + 2 C41 - C42 + C76 = 2
R41: C36 - C37 + C41 - C42 + C69 = 2
R45: C35 + 2 C36 - C37 + 2 C40 + 4 C41 - 2 C42 + C45 + 2 C46 - C47 = 2
R46: C36 - C37 + 2 C41 - 2 C42 + C46 - C47 + C74 = 2
R50: C0 + 2 C1 - C2 + 2 C5 + 4 C6 - 2 C7 - C10 - 2 C11 + C12 + C99 = 5
R51: C1 - C2 + 2 C6 - 2 C7 - C11 + C12 + C98 = 5
R54: - C2 - 2 C3 - C4 - 2 C7 - 4 C8 - 2 C9 + C12 + 2 C13 + C14 = 5
R55: C5 + 2 C6 - C7 - C10 - 2 C11 + C12 + C96 = 5
R56: C6 - C7 - C11 + C12 + C93 = 5
R63: C12 + C13 <= 5
R64: C12 + 2 C13 + C14 + C84 = 5
R67: C12 + C17 + C72 = 5
R68: C12 + C13 + C17 + C18 + C86 = 5
R69: C12 + 2 C13 + C14 + C17 + 2 C18 + C19 + C90 = 5
R72: C12 + 2 C17 + C22 + C79 = 5
R73: C12 + C13 + 2 C17 + 2 C18 + C22 + C23 + C88 = 5
R74: C12 + 2 C13 + C14 + 2 C17 + 4 C18 + 2 C19 + C22 + 2 C23 + C24 = 5
R76: C26 - C27 + 2 C31 - 2 C32 - C36 + C37 + C81 = 5
R79: - C27 - 2 C28 - C29 - 2 C32 - 4 C33 - 2 C34 + C37 + 2 C38 + C39 = 5
R80: C30 + 2 C31 - C32 - C35 - 2 C36 + C37 + C78 = 5
R81: C31 - C32 - C36 + C37 + C71 = 5
R88: C37 + C38 <= 5
R89: C37 + 2 C38 + C39 + C65 = 5
R92: C37 + C42 + C62 = 5
R93: C37 + C38 + C42 + C43 + C68 = 5
R94: C37 + 2 C38 + C39 + C42 + 2 C43 + C44 + C75 = 5
R97: C37 + 2 C42 + C47 + C64 = 5
R98: C37 + C38 + 2 C42 + 2 C43 + C47 + C48 + C73 = 5
R99: C37 + 2 C38 + C39 + 2 C42 + 4 C43 + 2 C44 + C47 + 2 C48 + C49 + C83
= 5
R100: C0 + C1 + 2 C5 + 2 C6 - C10 - C11 <= 0
R101: C5 + C6 - C10 - C11 <= 0
R102: - C10 - C11 <= 0
R103: - C10 - C11 - C15 - C16 <= 0
R104: - C10 - C11 - 2 C15 - 2 C16 - C20 - C21 <= 0
R105: C1 + 2 C6 - C11 <= 0
R106: C6 - C11 <= 0
R108: - C11 - C16 <= 0
R109: - C11 - 2 C16 - C21 <= 0
R110: C3 + 2 C8 - C13 <= 0
R111: C8 - C13 <= 0
R113: - C13 - C18 <= 0
R114: - C13 - 2 C18 - C23 <= 0
R115: C3 + C4 + 2 C8 + 2 C9 - C13 - C14 <= 0
R116: C8 + C9 - C13 - C14 <= 0
R117: - C13 - C14 <= 0
R118: - C13 - C14 - C18 - C19 <= 0
R119: - C13 - C14 - 2 C18 - 2 C19 - C23 - C24 <= 0
R120: C25 + C26 + 2 C30 + 2 C31 - C35 - C36 <= 0
R121: C30 + C31 - C35 - C36 <= 0
R122: - C35 - C36 <= 0
R123: - C35 - C36 - C40 - C41 <= 0
R124: - C35 - C36 - 2 C40 - 2 C41 - C45 - C46 <= 0
R125: C26 + 2 C31 - C36 <= 0
R126: C31 - C36 <= 0
R128: - C36 - C41 <= 0
R129: - C36 - 2 C41 - C46 <= 0
R130: C28 + 2 C33 - C38 <= 0
R131: C33 - C38 <= 0
R133: - C38 - C43 <= 0
R134: - C38 - 2 C43 - C48 <= 0
R135: C28 + C29 + 2 C33 + 2 C34 - C38 - C39 <= 0
R136: C33 + C34 - C38 - C39 <= 0
R137: - C38 - C39 <= 0
R138: - C38 - C39 - C43 - C44 <= 0
R139: - C38 - C39 - 2 C43 - 2 C44 - C48 - C49 <= 0
R84: 2 C0 - 0.2934222211687251 C0 - 0.6368296285761326 C1
+ 0.3434074074074074 C2 - 0.6368296285761326 C5 - 1.090266665086422 C6
+ 0.3117925925925931 C7 + 0.3434074074074074 C10
+ 0.3117925925925931 C11 + 0.4832888888888873 C12
- 1.516711111111112 C37 - 2.325125925925927 C38 - 0.8500740740740748 C39
- 2.325125925925927 C42 - 3.783659257679016 C43 - 1.48352592487243 C44
- 0.8500740740740748 C47 - 1.48352592487243 C48 - 0.6334518507983559 C49
= -2.378282933774724
R85: C0 - C1 = 1
R86: - C2 + 0.7071067811865476 C37 + 0.7118208263944582 C38
+ 0.1791337179005922 C39 + 0.7118208263944582 C42
+ 0.9522580833099196 C43 + 0.2993523463583229 C44
+ 0.1791337179005922 C47 + 0.2993523463583229 C48
+ 0.1202186284577307 C49 = 0
R87: - C3 + 0.3296796778800435 C38 + 0.2210053985528974 C39
+ 0.3296796778800435 C42 + 0.7803409156337385 C43
+ 0.4139534811809693 C44 + 0.2210053985528974 C47
+ 0.4139534811809693 C48 + 0.1929480826280727 C49 = 0
R88: - C4 + 0.1770449158331497 C38 + 0.0638367631462733 C39
+ 0.1770449158331497 C42 + 0.279120877220323 C43
+ 0.0638367631462772 C44 + 0.0638367631462733 C47
+ 0.0638367631462772 C48 = 0
R89: - C5 + 0.1585172757764243 C38 + 0.1585172757764243 C42
+ 0.1820695436282836 C43 = 0
R90: - C6 + 0.038703233847106 C38 + 0.038703233847106 C42 = 0
R91: - C7 + 0.2273356136158768 C0 + 0.5096397223166684 C1
- 0.2823041087007916 C2 + 0.5096397223166684 C5 + 1.165872957454474 C6
- 0.656233235137806 C7 - 0.2823041087007916 C10 - 0.656233235137806 C11
+ 0.3739291264370143 C12 = 0
R92: - C8 + 0.0351662521327694 C1 - 0.0351662521327693 C2
+ 0.0351662521327694 C5 + 0.3955599182393737 C6 - 0.4298087016296293 C7
- 0.0351662521327693 C10 - 0.4298087016296293 C11
+ 0.6001474888742361 C12 = 0
R93: - C9 - 0.0469408052137706 C1 + 0.0469408052137704 C2
- 0.0469408052137706 C5 - 0.3251146163415241 C6 + 0.240770781558248 C7
+ 0.0469408052137704 C10 + 0.2407707815582481 C11 = 0
R94: - C10 - 0.0432630689488897 C1 + 0.0432630689488896 C2
- 0.0432630689488897 C5 - 0.0591042547970414 C6 + 0.0432630689488896 C10
= 0
R95: - C11 + 0.0431851377587622 C6 = 0
cone0: [ - C0 ^2 + C1 ^2 + C2 ^2 + C3 ^2 + C4 ^2 + C5 ^2 + C6 ^2 + C7 ^2
+ C8 ^2 + C9 ^2 + C10 ^2 + C11 ^2 ] <= 0
Bounds
C1 free
C2 free
C3 free
C4 free
C5 free
C6 free
C7 free
C8 free
C9 free
C10 free
C11 free
C0 free
C1 free
C2 free
-infinity <= C3 <= 35.036
C4 free
C5 free
C6 free
C7 free
-infinity <= C8 <= 7.008
-infinity <= C9 <= 28.029
C10 free
-2 <= C12 <= 5
-infinity <= C14 <= 7.008
C15 free
C16 >= -7.008
-infinity <= C17 <= 7.008
-infinity <= C18 <= 14.015
C19 >= -28.029
C20 free
C21 free
-infinity <= C22 <= 21.022
C23 >= -35.036
C24 free
C25 free
C26 free
C27 >= -21.022
-infinity <= C28 <= 35.036
C29 free
C30 free
-infinity <= C31 <= 7.008
-infinity <= C32 <= 7.008
-infinity <= C33 <= 7.008
-infinity <= C34 <= 28.029
-infinity <= C35 <= 7.008
-2 <= C37 <= 5
C39 free
C40 free
C41 >= -7.008
C42 free
C43 free
C44 free
C45 free
C46 free
C47 free
C48 free
C49 free
C62 <= 7
C63 <= 7
C64 <= 7
C65 <= 7
C66 <= 7
C67 <= 7
C68 <= 7
C69 <= 7
C70 <= 7
C71 <= 7
C72 <= 7
C73 <= 7
C74 <= 7
C75 <= 7
C76 <= 7
C77 <= 7
C78 <= 7
C79 <= 7
C80 <= 7
C81 <= 7
C82 <= 7
C83 <= 7
C84 <= 7
C85 <= 7
C86 <= 7
C87 <= 7
C88 <= 7
C89 <= 7
C90 <= 7
C91 <= 7
C92 <= 7
C93 <= 7
C94 <= 7
C95 <= 7
C96 <= 7
C97 <= 7
C98 <= 7
C99 <= 7
End
3. log of the larger model
Gurobi 9.1.2 (mac64, R) logging started Tue Sep 7 15:02:24 2021
Academic license - for non-commercial use only - expires 2022-08-03
Gurobi Optimizer version 9.1.2 build v9.1.2rc0 (mac64)
Thread count: 4 physical cores, 8 logical processors, using up to 8 threads
Optimize a model with 141 rows, 50 columns and 622 nonzeros
Model fingerprint: 0x06aace94
Model has 1 quadratic constraint
Coefficient statistics:
Matrix range [1e+00, 4e+00]
QMatrix range [5e-02, 2e+00]
QLMatrix range [3e-01, 4e+00]
Objective range [1e+00, 1e+00]
Bounds range [0e+00, 0e+00]
RHS range [2e+00, 5e+00]
QRHS range [3e+00, 3e+00]
Presolve removed 56 rows and 0 columns
Presolve time: 0.00s
Presolved: 97 rows, 100 columns, 502 nonzeros
Presolved model has 1 second-order cone constraint
Ordering time: 0.00s
Barrier statistics:
AA' NZ : 1.462e+03
Factor NZ : 1.669e+03
Factor Ops : 3.270e+04 (less than 1 second per iteration)
Threads : 1
Objective Residual
Iter Primal Dual Primal Dual Compl Time
0 -1.34478232e+01 -1.10307644e+03 1.35e+03 7.02e-01 2.59e+02 0s
1 -7.41878044e+01 -3.22130278e+02 3.50e+02 2.53e-02 6.07e+01 0s
2 -5.07692724e+00 -2.46971408e+02 1.32e+01 2.79e-08 3.66e+00 0s
3 -3.75642561e+00 -7.73744037e+01 2.81e+00 1.39e-09 7.66e-01 0s
4 -2.91152704e+00 -2.49055543e+01 1.12e+00 9.98e-11 2.08e-01 0s
5 -1.39474290e+00 -9.97531978e+00 4.17e-01 2.04e-11 7.25e-02 0s
6 -1.25692798e+00 -6.20057079e+00 3.17e-01 8.57e-12 4.21e-02 0s
7 -7.04958628e-01 -4.51860745e+00 2.37e-01 5.38e-12 3.20e-02 0s
8 -4.70736907e-01 -2.70383624e+00 1.80e-01 2.91e-12 2.06e-02 0s
9 7.26477565e-01 2.44912442e-01 4.78e-02 1.90e-13 6.65e-03 0s
10 1.05997678e+00 1.38316625e+00 2.52e-02 9.95e-14 3.64e-03 0s
11 1.71662185e+00 1.79432155e+00 2.50e-03 2.56e-13 3.14e-04 0s
12 1.74890180e+00 1.84560985e+00 1.80e-03 3.92e-12 8.71e-05 0s
13 1.75473917e+00 1.86851231e+00 1.68e-03 2.85e-11 5.15e-05 0s
14 1.79447970e+00 1.89298311e+00 4.50e-04 4.99e-10 2.73e-05 0s
15 1.81042664e+00 1.91280049e+00 3.77e-04 3.82e-10 5.54e-05 0s
16 1.82774875e+00 1.91455691e+00 1.95e-04 2.00e-09 1.50e-05 0s
17 1.84269145e+00 1.91519456e+00 1.59e-04 1.82e-10 1.10e-06 0s
18 1.84205278e+00 1.91482007e+00 1.37e-04 6.33e-09 6.26e-08 0s
19 1.84178624e+00 1.91482449e+00 1.61e-04 1.17e-07 1.08e-09 0s
20 1.84182471e+00 1.91482455e+00 1.61e-04 6.31e-06 5.31e-12 0s
21 1.84182595e+00 1.91482455e+00 8.03e-05 2.06e-06 5.68e-12 0s
22 1.84182305e+00 1.91482456e+00 9.40e-05 9.20e-06 1.03e-11 0s
23 1.84180701e+00 1.91482457e+00 2.17e-04 2.19e-05 4.63e-11 0s
24 1.84182952e+00 1.91482457e+00 1.20e-04 2.62e-06 5.08e-12 0s
25 1.84183011e+00 1.91482457e+00 9.67e-05 9.80e-06 4.20e-12 0s
26 1.84183028e+00 1.91482457e+00 1.28e-04 1.87e-05 3.72e-12 0s
27 1.84183046e+00 1.91482458e+00 9.90e-05 3.83e-05 6.44e-12 0s
28 1.84183002e+00 1.91482458e+00 1.08e-04 3.89e-05 4.38e-10 0s
29 1.84183031e+00 1.91482458e+00 8.60e-05 7.76e-05 1.32e-11 0s
30 1.84184695e+00 1.91482469e+00 1.34e-04 7.66e-06 2.96e-10 0s
31 1.84187710e+00 1.91482526e+00 1.21e-04 3.39e-06 3.37e-10 0s
32 1.84184649e+00 1.91482995e+00 1.03e-04 7.15e-06 1.48e-10 0s
33 1.84184422e+00 1.91482995e+00 1.48e-04 1.23e-05 5.39e-11 0s
34 1.84181504e+00 1.91482955e+00 1.82e-04 5.18e-08 1.93e-10 0s
35 1.84198128e+00 1.91483138e+00 1.88e-04 6.58e-06 1.10e-10 0s
36 1.84178039e+00 1.91483057e+00 1.34e-04 1.29e-05 2.40e-10 0s
37 1.84190110e+00 1.91482862e+00 1.80e-04 2.60e-05 3.44e-10 0s
38 1.84181524e+00 1.91477096e+00 1.62e-04 2.00e-05 9.10e-11 0s
39 1.84173035e+00 1.91477015e+00 1.17e-04 3.84e-05 3.86e-10 0s
40 1.84181275e+00 1.91478415e+00 9.10e-05 4.33e-06 2.04e-11 0s
41 1.84180982e+00 1.91478262e+00 1.71e-04 4.63e-06 2.48e-11 0s
42 1.84179875e+00 1.91478237e+00 2.63e-04 3.26e-07 3.36e-11 0s
43 1.84207421e+00 1.91478530e+00 1.55e-04 6.51e-06 4.46e-10 0s
44 1.84177159e+00 1.91478530e+00 1.56e-04 8.33e-07 1.00e-10 0s
45 1.84173465e+00 1.91478418e+00 8.32e-05 6.12e-06 1.86e-10 0s
46 1.84174639e+00 1.91478418e+00 1.54e-04 8.24e-06 1.15e-10 0s
47 1.84174389e+00 1.91478419e+00 1.47e-04 1.44e-05 4.93e-11 0s
48 1.84174383e+00 1.91478419e+00 1.51e-04 2.15e-05 4.66e-11 0s
49 1.84174379e+00 1.91478419e+00 1.56e-04 3.15e-05 4.33e-11 0s
50 1.84174374e+00 1.91478419e+00 1.59e-04 5.01e-05 3.45e-11 0s
51 1.84174297e+00 1.91478421e+00 2.36e-04 1.04e-04 6.17e-11 0s
Barrier solved model in 51 iterations and 0.01 seconds
Optimal objective 1.84182952e+00
4. lp file after presolving the larger model
\ Model R
\ LP format - for model browsing. Use MPS format to capture full model detail.
Minimize
- C12 + C37
Subject To
R0: C0 + 2 C1 - C2 + 2 C5 + 4 C6 - 2 C7 - C10 - 2 C11 + C12 >= -2
R1: C1 - C2 + 2 C6 - 2 C7 - C11 + C12 >= -2
R2: - C2 - 2 C7 + C12 >= -2
R3: - C2 - C3 - 2 C7 - 2 C8 + C12 + C13 >= -2
R4: - C2 - 2 C3 - C4 - 2 C7 - 4 C8 - 2 C9 + C12 + 2 C13 + C14 >= -2
R5: C5 + 2 C6 - C7 - C10 - 2 C11 + C12 >= -2
R6: C6 - C7 - C11 + C12 >= -2
R7: - C7 + C12 >= -2
R8: - C7 - C8 + C12 + C13 >= -2
R9: - C7 - 2 C8 - C9 + C12 + 2 C13 + C14 >= -2
R10: - C10 - 2 C11 + C12 >= -2
R11: - C11 + C12 >= -2
R12: C12 >= -2
R13: C12 + C13 >= -2
R14: C12 + 2 C13 + C14 >= -2
R15: - C10 - 2 C11 + C12 - C15 - 2 C16 + C17 >= -2
R16: - C11 + C12 - C16 + C17 >= -2
R17: C12 + C17 >= -2
R18: C12 + C13 + C17 + C18 >= -2
R19: C12 + 2 C13 + C14 + C17 + 2 C18 + C19 >= -2
R20: - C10 - 2 C11 + C12 - 2 C15 - 4 C16 + 2 C17 - C20 - 2 C21 + C22
>= -2
R21: - C11 + C12 - 2 C16 + 2 C17 - C21 + C22 >= -2
R22: C12 + 2 C17 + C22 >= -2
R23: C12 + C13 + 2 C17 + 2 C18 + C22 + C23 >= -2
R24: C12 + 2 C13 + C14 + 2 C17 + 4 C18 + 2 C19 + C22 + 2 C23 + C24 >= -2
R25: C25 + 2 C26 - C27 + 2 C30 + 4 C31 - 2 C32 - C35 - 2 C36 + C37 >= -2
R26: C26 - C27 + 2 C31 - 2 C32 - C36 + C37 >= -2
R27: - C27 - 2 C32 + C37 >= -2
R28: - C27 - C28 - 2 C32 - 2 C33 + C37 + C38 >= -2
R29: - C27 - 2 C28 - C29 - 2 C32 - 4 C33 - 2 C34 + C37 + 2 C38 + C39
>= -2
R30: C30 + 2 C31 - C32 - C35 - 2 C36 + C37 >= -2
R31: C31 - C32 - C36 + C37 >= -2
R32: - C32 + C37 >= -2
R33: - C32 - C33 + C37 + C38 >= -2
R34: - C32 - 2 C33 - C34 + C37 + 2 C38 + C39 >= -2
R35: - C35 - 2 C36 + C37 >= -2
R36: - C36 + C37 >= -2
R37: C37 >= -2
R38: C37 + C38 >= -2
R39: C37 + 2 C38 + C39 >= -2
R40: - C35 - 2 C36 + C37 - C40 - 2 C41 + C42 >= -2
R41: - C36 + C37 - C41 + C42 >= -2
R42: C37 + C42 >= -2
R43: C37 + C38 + C42 + C43 >= -2
R44: C37 + 2 C38 + C39 + C42 + 2 C43 + C44 >= -2
R45: - C35 - 2 C36 + C37 - 2 C40 - 4 C41 + 2 C42 - C45 - 2 C46 + C47
>= -2
R46: - C36 + C37 - 2 C41 + 2 C42 - C46 + C47 >= -2
R47: C37 + 2 C42 + C47 >= -2
R48: C37 + C38 + 2 C42 + 2 C43 + C47 + C48 >= -2
R49: C37 + 2 C38 + C39 + 2 C42 + 4 C43 + 2 C44 + C47 + 2 C48 + C49 >= -2
R50: C0 + 2 C1 - C2 + 2 C5 + 4 C6 - 2 C7 - C10 - 2 C11 + C12 <= 5
R51: C1 - C2 + 2 C6 - 2 C7 - C11 + C12 <= 5
R52: - C2 - 2 C7 + C12 <= 5
R53: - C2 - C3 - 2 C7 - 2 C8 + C12 + C13 <= 5
R54: - C2 - 2 C3 - C4 - 2 C7 - 4 C8 - 2 C9 + C12 + 2 C13 + C14 <= 5
R55: C5 + 2 C6 - C7 - C10 - 2 C11 + C12 <= 5
R56: C6 - C7 - C11 + C12 <= 5
R57: - C7 + C12 <= 5
R58: - C7 - C8 + C12 + C13 <= 5
R59: - C7 - 2 C8 - C9 + C12 + 2 C13 + C14 <= 5
R60: - C10 - 2 C11 + C12 <= 5
R61: - C11 + C12 <= 5
R62: C12 <= 5
R63: C12 + C13 <= 5
R64: C12 + 2 C13 + C14 <= 5
R65: - C10 - 2 C11 + C12 - C15 - 2 C16 + C17 <= 5
R66: - C11 + C12 - C16 + C17 <= 5
R67: C12 + C17 <= 5
R68: C12 + C13 + C17 + C18 <= 5
R69: C12 + 2 C13 + C14 + C17 + 2 C18 + C19 <= 5
R70: - C10 - 2 C11 + C12 - 2 C15 - 4 C16 + 2 C17 - C20 - 2 C21 + C22 <= 5
R71: - C11 + C12 - 2 C16 + 2 C17 - C21 + C22 <= 5
R72: C12 + 2 C17 + C22 <= 5
R73: C12 + C13 + 2 C17 + 2 C18 + C22 + C23 <= 5
R74: C12 + 2 C13 + C14 + 2 C17 + 4 C18 + 2 C19 + C22 + 2 C23 + C24 <= 5
R75: C25 + 2 C26 - C27 + 2 C30 + 4 C31 - 2 C32 - C35 - 2 C36 + C37 <= 5
R76: C26 - C27 + 2 C31 - 2 C32 - C36 + C37 <= 5
R77: - C27 - 2 C32 + C37 <= 5
R78: - C27 - C28 - 2 C32 - 2 C33 + C37 + C38 <= 5
R79: - C27 - 2 C28 - C29 - 2 C32 - 4 C33 - 2 C34 + C37 + 2 C38 + C39 <= 5
R80: C30 + 2 C31 - C32 - C35 - 2 C36 + C37 <= 5
R81: C31 - C32 - C36 + C37 <= 5
R82: - C32 + C37 <= 5
R83: - C32 - C33 + C37 + C38 <= 5
R84: - C32 - 2 C33 - C34 + C37 + 2 C38 + C39 <= 5
R85: - C35 - 2 C36 + C37 <= 5
R86: - C36 + C37 <= 5
R87: C37 <= 5
R88: C37 + C38 <= 5
R89: C37 + 2 C38 + C39 <= 5
R90: - C35 - 2 C36 + C37 - C40 - 2 C41 + C42 <= 5
R91: - C36 + C37 - C41 + C42 <= 5
R92: C37 + C42 <= 5
R93: C37 + C38 + C42 + C43 <= 5
R94: C37 + 2 C38 + C39 + C42 + 2 C43 + C44 <= 5
R95: - C35 - 2 C36 + C37 - 2 C40 - 4 C41 + 2 C42 - C45 - 2 C46 + C47 <= 5
R96: - C36 + C37 - 2 C41 + 2 C42 - C46 + C47 <= 5
R97: C37 + 2 C42 + C47 <= 5
R98: C37 + C38 + 2 C42 + 2 C43 + C47 + C48 <= 5
R99: C37 + 2 C38 + C39 + 2 C42 + 4 C43 + 2 C44 + C47 + 2 C48 + C49 <= 5
R100: - C0 - C1 - 2 C5 - 2 C6 + C10 + C11 >= 0
R101: - C5 - C6 + C10 + C11 >= 0
R102: C10 + C11 >= 0
R103: C10 + C11 + C15 + C16 >= 0
R104: C10 + C11 + 2 C15 + 2 C16 + C20 + C21 >= 0
R105: - C1 - 2 C6 + C11 >= 0
R106: - C6 + C11 >= 0
R107: C11 >= 0
R108: C11 + C16 >= 0
R109: C11 + 2 C16 + C21 >= 0
R110: - C3 - 2 C8 + C13 >= 0
R111: - C8 + C13 >= 0
R112: C13 >= 0
R113: C13 + C18 >= 0
R114: C13 + 2 C18 + C23 >= 0
R115: - C3 - C4 - 2 C8 - 2 C9 + C13 + C14 >= 0
R116: - C8 - C9 + C13 + C14 >= 0
R117: C13 + C14 >= 0
R118: C13 + C14 + C18 + C19 >= 0
R119: C13 + C14 + 2 C18 + 2 C19 + C23 + C24 >= 0
R120: - C25 - C26 - 2 C30 - 2 C31 + C35 + C36 >= 0
R121: - C30 - C31 + C35 + C36 >= 0
R122: C35 + C36 >= 0
R123: C35 + C36 + C40 + C41 >= 0
R124: C35 + C36 + 2 C40 + 2 C41 + C45 + C46 >= 0
R125: - C26 - 2 C31 + C36 >= 0
R126: - C31 + C36 >= 0
R127: C36 >= 0
R128: C36 + C41 >= 0
R129: C36 + 2 C41 + C46 >= 0
R130: - C28 - 2 C33 + C38 >= 0
R131: - C33 + C38 >= 0
R132: C38 >= 0
R133: C38 + C43 >= 0
R134: C38 + 2 C43 + C48 >= 0
R135: - C28 - C29 - 2 C33 - 2 C34 + C38 + C39 >= 0
R136: - C33 - C34 + C38 + C39 >= 0
R137: C38 + C39 >= 0
R138: C38 + C39 + C43 + C44 >= 0
R139: C38 + C39 + 2 C43 + 2 C44 + C48 + C49 >= 0
R140: - C0 - 2 C1 - 2 C5 - 4 C6 + C10 + 2 C11 >= 0
Step_1_Constraint: - 0.2934222211687251 C0 - 0.6368296285761326 C1
+ 0.3434074074074074 C2 - 0.6368296285761326 C5 - 1.090266665086422 C6
+ 0.3117925925925931 C7 + 0.3434074074074074 C10
+ 0.3117925925925931 C11 + 0.4832888888888873 C12
- 1.516711111111112 C37 - 2.325125925925927 C38 - 0.8500740740740748 C39
- 2.325125925925927 C42 - 3.783659257679016 C43 - 1.48352592487243 C44
- 0.8500740740740748 C47 - 1.48352592487243 C48 - 0.6334518507983559 C49
+ [ 0.0516814812181072 C0 ^2 + 0.2317185179917698 C0 * C1
- 0.1283555555555553 C0 * C2 + 0.2317185179917698 C0 * C5
+ 0.53008888836214 C0 * C6 - 0.2983703703703702 C0 * C7
- 0.1283555555555553 C0 * C10 - 0.2983703703703702 C0 * C11
+ 0.1700148148148148 C0 * C12 + 0.26504444418107 C1 ^2
- 0.2983703703703702 C1 * C2 + 0.53008888836214 C1 * C5
+ 1.251807406880658 C1 * C6 - 0.7217185185185184 C1 * C7
- 0.2983703703703702 C1 * C10 - 0.7217185185185184 C1 * C11
+ 0.4233481481481483 C1 * C12 + 0.0850074074074074 C2 ^2
- 0.2983703703703702 C2 * C5 - 0.7217185185185184 C2 * C6
+ 0.4233481481481483 C2 * C7 + 0.1700148148148148 C2 * C10
+ 0.4233481481481483 C2 * C11 - 0.2533333333333334 C2 * C12
+ 0.26504444418107 C5 ^2 + 1.251807406880658 C5 * C6
- 0.7217185185185184 C5 * C7 - 0.2983703703703702 C5 * C10
- 0.7217185185185184 C5 * C11 + 0.4233481481481483 C5 * C12
+ 1.626785184658436 C6 ^2 - 2.026755555555555 C6 * C7
- 0.7217185185185184 C6 * C10 - 2.026755555555555 C6 * C11
+ 1.346696296296297 C6 * C12 + 0.6733481481481483 C7 ^2
+ 0.4233481481481483 C7 * C10 + 1.346696296296297 C7 * C11
- 1.006666666666667 C7 * C12 + 0.0850074074074074 C10 ^2
+ 0.4233481481481483 C10 * C11 - 0.2533333333333334 C10 * C12
+ 0.6733481481481483 C11 ^2 - 1.006666666666667 C11 * C12 + 0.5 C12 ^2
+ 0.5 C37 ^2 + 1.006666666666667 C37 * C38
+ 0.2533333333333335 C37 * C39 + 1.006666666666667 C37 * C42
+ 1.346696296296297 C37 * C43 + 0.4233481481481484 C37 * C44
+ 0.2533333333333335 C37 * C47 + 0.4233481481481484 C37 * C48
+ 0.1700148148148148 C37 * C49 + 0.6733481481481484 C38 ^2
+ 0.4233481481481484 C38 * C39 + 1.346696296296297 C38 * C42
+ 2.026755555555556 C38 * C43 + 0.7217185185185189 C38 * C44
+ 0.4233481481481484 C38 * C47 + 0.7217185185185189 C38 * C48
+ 0.2983703703703704 C38 * C49 + 0.0850074074074074 C39 ^2
+ 0.4233481481481484 C39 * C42 + 0.7217185185185189 C39 * C43
+ 0.2983703703703705 C39 * C44 + 0.1700148148148148 C39 * C47
+ 0.2983703703703705 C39 * C48 + 0.1283555555555556 C39 * C49
+ 0.6733481481481484 C42 ^2 + 2.026755555555556 C42 * C43
+ 0.7217185185185189 C42 * C44 + 0.4233481481481484 C42 * C47
+ 0.7217185185185189 C42 * C48 + 0.2983703703703704 C42 * C49
+ 1.626785184658437 C43 ^2 + 1.25180740688066 C43 * C44
+ 0.7217185185185189 C43 * C47 + 1.25180740688066 C43 * C48
+ 0.5300888883621409 C43 * C49 + 0.2650444441810703 C44 ^2
+ 0.2983703703703705 C44 * C47 + 0.5300888883621406 C44 * C48
+ 0.2317185179917702 C44 * C49 + 0.0850074074074074 C47 ^2
+ 0.2983703703703705 C47 * C48 + 0.1283555555555556 C47 * C49
+ 0.2650444441810703 C48 ^2 + 0.2317185179917702 C48 * C49
+ 0.0516814812181075 C49 ^2 ] <= -3.378282933774724
Bounds
C0 free
C1 free
C2 free
C3 free
C4 free
C5 free
C6 free
C7 free
C8 free
C9 free
C10 free
C11 free
C12 free
C13 free
C14 free
C15 free
C16 free
C17 free
C18 free
C19 free
C20 free
C21 free
C22 free
C23 free
C24 free
C25 free
C26 free
C27 free
C28 free
C29 free
C30 free
C31 free
C32 free
C33 free
C34 free
C35 free
C36 free
C37 free
C38 free
C39 free
C40 free
C41 free
C42 free
C43 free
C44 free
C45 free
C46 free
C47 free
C48 free
C49 free
End
0
-
Hi Omkar,
Thanks for raising this. I believe it's not too unusual for some redundant constraints to make it through presolve, as checking redundancy for all subsets of constraints can be expensive but have limited benefits for the solver. However it is not expected that the optimal solution values would differ.
Could you please share the original models? As you point out the presolved results you have posted here are very different models (actually when I run these, the first appears to be non-convex infeasible, and the second convex and feasible) so it would help to see the original source.0 -
Hi Simon,
Thanks for your response. Below, I copy-pasted the contents to the mps files for the smaller and larger models -- let me know if there is a better way to share the original models. In case it helps, I used a diff tool to verify that the only differences between the two models are related to R140, i.e., the redundant constraint (see picture below).
Smaller Model (step2_minimal.mps)
NAME R
ROWS
N OBJ
G R0
G R1
G R2
G R3
G R4
G R5
G R6
G R7
G R8
G R9
G R10
G R11
G R12
G R13
G R14
G R15
G R16
G R17
G R18
G R19
G R20
G R21
G R22
G R23
G R24
G R25
G R26
G R27
G R28
G R29
G R30
G R31
G R32
G R33
G R34
G R35
G R36
G R37
G R38
G R39
G R40
G R41
G R42
G R43
G R44
G R45
G R46
G R47
G R48
G R49
L R50
L R51
L R52
L R53
L R54
L R55
L R56
L R57
L R58
L R59
L R60
L R61
L R62
L R63
L R64
L R65
L R66
L R67
L R68
L R69
L R70
L R71
L R72
L R73
L R74
L R75
L R76
L R77
L R78
L R79
L R80
L R81
L R82
L R83
L R84
L R85
L R86
L R87
L R88
L R89
L R90
L R91
L R92
L R93
L R94
L R95
L R96
L R97
L R98
L R99
G R100
G R101
G R102
G R103
G R104
G R105
G R106
G R107
G R108
G R109
G R110
G R111
G R112
G R113
G R114
G R115
G R116
G R117
G R118
G R119
G R120
G R121
G R122
G R123
G R124
G R125
G R126
G R127
G R128
G R129
G R130
G R131
G R132
G R133
G R134
G R135
G R136
G R137
G R138
G R139
L qc0
COLUMNS
C0 R0 1
C0 R50 1
C0 R100 -1
C0 qc0 -2.9342222116872513e-01
C1 R0 2
C1 R1 1
C1 R50 2
C1 R51 1
C1 R100 -1
C1 R105 -1
C1 qc0 -6.3682962857613257e-01
C2 R0 -1
C2 R1 -1
C2 R2 -1
C2 R3 -1
C2 R4 -1
C2 R50 -1
C2 R51 -1
C2 R52 -1
C2 R53 -1
C2 R54 -1
C2 qc0 3.4340740740740738e-01
C3 R3 -1
C3 R4 -2
C3 R53 -1
C3 R54 -2
C3 R110 -1
C3 R115 -1
C4 R4 -1
C4 R54 -1
C4 R115 -1
C5 R0 2
C5 R5 1
C5 R50 2
C5 R55 1
C5 R100 -2
C5 R101 -1
C5 qc0 -6.3682962857613257e-01
C6 R0 4
C6 R1 2
C6 R5 2
C6 R6 1
C6 R50 4
C6 R51 2
C6 R55 2
C6 R56 1
C6 R100 -2
C6 R101 -1
C6 R105 -2
C6 R106 -1
C6 qc0 -1.0902666650864219e+00
C7 R0 -2
C7 R1 -2
C7 R2 -2
C7 R3 -2
C7 R4 -2
C7 R5 -1
C7 R6 -1
C7 R7 -1
C7 R8 -1
C7 R9 -1
C7 R50 -2
C7 R51 -2
C7 R52 -2
C7 R53 -2
C7 R54 -2
C7 R55 -1
C7 R56 -1
C7 R57 -1
C7 R58 -1
C7 R59 -1
C7 qc0 3.1179259259259307e-01
C8 R3 -2
C8 R4 -4
C8 R8 -1
C8 R9 -2
C8 R53 -2
C8 R54 -4
C8 R58 -1
C8 R59 -2
C8 R110 -2
C8 R111 -1
C8 R115 -2
C8 R116 -1
C9 R4 -2
C9 R9 -1
C9 R54 -2
C9 R59 -1
C9 R115 -2
C9 R116 -1
C10 R0 -1
C10 R5 -1
C10 R10 -1
C10 R15 -1
C10 R20 -1
C10 R50 -1
C10 R55 -1
C10 R60 -1
C10 R65 -1
C10 R70 -1
C10 R100 1
C10 R101 1
C10 R102 1
C10 R103 1
C10 R104 1
C10 qc0 3.4340740740740738e-01
C11 R0 -2
C11 R1 -1
C11 R5 -2
C11 R6 -1
C11 R10 -2
C11 R11 -1
C11 R15 -2
C11 R16 -1
C11 R20 -2
C11 R21 -1
C11 R50 -2
C11 R51 -1
C11 R55 -2
C11 R56 -1
C11 R60 -2
C11 R61 -1
C11 R65 -2
C11 R66 -1
C11 R70 -2
C11 R71 -1
C11 R100 1
C11 R101 1
C11 R102 1
C11 R103 1
C11 R104 1
C11 R105 1
C11 R106 1
C11 R107 1
C11 R108 1
C11 R109 1
C11 qc0 3.1179259259259307e-01
C12 OBJ -1
C12 R0 1
C12 R1 1
C12 R2 1
C12 R3 1
C12 R4 1
C12 R5 1
C12 R6 1
C12 R7 1
C12 R8 1
C12 R9 1
C12 R10 1
C12 R11 1
C12 R12 1
C12 R13 1
C12 R14 1
C12 R15 1
C12 R16 1
C12 R17 1
C12 R18 1
C12 R19 1
C12 R20 1
C12 R21 1
C12 R22 1
C12 R23 1
C12 R24 1
C12 R50 1
C12 R51 1
C12 R52 1
C12 R53 1
C12 R54 1
C12 R55 1
C12 R56 1
C12 R57 1
C12 R58 1
C12 R59 1
C12 R60 1
C12 R61 1
C12 R62 1
C12 R63 1
C12 R64 1
C12 R65 1
C12 R66 1
C12 R67 1
C12 R68 1
C12 R69 1
C12 R70 1
C12 R71 1
C12 R72 1
C12 R73 1
C12 R74 1
C12 qc0 4.8328888888888732e-01
C13 R3 1
C13 R4 2
C13 R8 1
C13 R9 2
C13 R13 1
C13 R14 2
C13 R18 1
C13 R19 2
C13 R23 1
C13 R24 2
C13 R53 1
C13 R54 2
C13 R58 1
C13 R59 2
C13 R63 1
C13 R64 2
C13 R68 1
C13 R69 2
C13 R73 1
C13 R74 2
C13 R110 1
C13 R111 1
C13 R112 1
C13 R113 1
C13 R114 1
C13 R115 1
C13 R116 1
C13 R117 1
C13 R118 1
C13 R119 1
C14 R4 1
C14 R9 1
C14 R14 1
C14 R19 1
C14 R24 1
C14 R54 1
C14 R59 1
C14 R64 1
C14 R69 1
C14 R74 1
C14 R115 1
C14 R116 1
C14 R117 1
C14 R118 1
C14 R119 1
C15 R15 -1
C15 R20 -2
C15 R65 -1
C15 R70 -2
C15 R103 1
C15 R104 2
C16 R15 -2
C16 R16 -1
C16 R20 -4
C16 R21 -2
C16 R65 -2
C16 R66 -1
C16 R70 -4
C16 R71 -2
C16 R103 1
C16 R104 2
C16 R108 1
C16 R109 2
C17 R15 1
C17 R16 1
C17 R17 1
C17 R18 1
C17 R19 1
C17 R20 2
C17 R21 2
C17 R22 2
C17 R23 2
C17 R24 2
C17 R65 1
C17 R66 1
C17 R67 1
C17 R68 1
C17 R69 1
C17 R70 2
C17 R71 2
C17 R72 2
C17 R73 2
C17 R74 2
C18 R18 1
C18 R19 2
C18 R23 2
C18 R24 4
C18 R68 1
C18 R69 2
C18 R73 2
C18 R74 4
C18 R113 1
C18 R114 2
C18 R118 1
C18 R119 2
C19 R19 1
C19 R24 2
C19 R69 1
C19 R74 2
C19 R118 1
C19 R119 2
C20 R20 -1
C20 R70 -1
C20 R104 1
C21 R20 -2
C21 R21 -1
C21 R70 -2
C21 R71 -1
C21 R104 1
C21 R109 1
C22 R20 1
C22 R21 1
C22 R22 1
C22 R23 1
C22 R24 1
C22 R70 1
C22 R71 1
C22 R72 1
C22 R73 1
C22 R74 1
C23 R23 1
C23 R24 2
C23 R73 1
C23 R74 2
C23 R114 1
C23 R119 1
C24 R24 1
C24 R74 1
C24 R119 1
C25 R25 1
C25 R75 1
C25 R120 -1
C26 R25 2
C26 R26 1
C26 R75 2
C26 R76 1
C26 R120 -1
C26 R125 -1
C27 R25 -1
C27 R26 -1
C27 R27 -1
C27 R28 -1
C27 R29 -1
C27 R75 -1
C27 R76 -1
C27 R77 -1
C27 R78 -1
C27 R79 -1
C28 R28 -1
C28 R29 -2
C28 R78 -1
C28 R79 -2
C28 R130 -1
C28 R135 -1
C29 R29 -1
C29 R79 -1
C29 R135 -1
C30 R25 2
C30 R30 1
C30 R75 2
C30 R80 1
C30 R120 -2
C30 R121 -1
C31 R25 4
C31 R26 2
C31 R30 2
C31 R31 1
C31 R75 4
C31 R76 2
C31 R80 2
C31 R81 1
C31 R120 -2
C31 R121 -1
C31 R125 -2
C31 R126 -1
C32 R25 -2
C32 R26 -2
C32 R27 -2
C32 R28 -2
C32 R29 -2
C32 R30 -1
C32 R31 -1
C32 R32 -1
C32 R33 -1
C32 R34 -1
C32 R75 -2
C32 R76 -2
C32 R77 -2
C32 R78 -2
C32 R79 -2
C32 R80 -1
C32 R81 -1
C32 R82 -1
C32 R83 -1
C32 R84 -1
C33 R28 -2
C33 R29 -4
C33 R33 -1
C33 R34 -2
C33 R78 -2
C33 R79 -4
C33 R83 -1
C33 R84 -2
C33 R130 -2
C33 R131 -1
C33 R135 -2
C33 R136 -1
C34 R29 -2
C34 R34 -1
C34 R79 -2
C34 R84 -1
C34 R135 -2
C34 R136 -1
C35 R25 -1
C35 R30 -1
C35 R35 -1
C35 R40 -1
C35 R45 -1
C35 R75 -1
C35 R80 -1
C35 R85 -1
C35 R90 -1
C35 R95 -1
C35 R120 1
C35 R121 1
C35 R122 1
C35 R123 1
C35 R124 1
C36 R25 -2
C36 R26 -1
C36 R30 -2
C36 R31 -1
C36 R35 -2
C36 R36 -1
C36 R40 -2
C36 R41 -1
C36 R45 -2
C36 R46 -1
C36 R75 -2
C36 R76 -1
C36 R80 -2
C36 R81 -1
C36 R85 -2
C36 R86 -1
C36 R90 -2
C36 R91 -1
C36 R95 -2
C36 R96 -1
C36 R120 1
C36 R121 1
C36 R122 1
C36 R123 1
C36 R124 1
C36 R125 1
C36 R126 1
C36 R127 1
C36 R128 1
C36 R129 1
C37 OBJ 1
C37 R25 1
C37 R26 1
C37 R27 1
C37 R28 1
C37 R29 1
C37 R30 1
C37 R31 1
C37 R32 1
C37 R33 1
C37 R34 1
C37 R35 1
C37 R36 1
C37 R37 1
C37 R38 1
C37 R39 1
C37 R40 1
C37 R41 1
C37 R42 1
C37 R43 1
C37 R44 1
C37 R45 1
C37 R46 1
C37 R47 1
C37 R48 1
C37 R49 1
C37 R75 1
C37 R76 1
C37 R77 1
C37 R78 1
C37 R79 1
C37 R80 1
C37 R81 1
C37 R82 1
C37 R83 1
C37 R84 1
C37 R85 1
C37 R86 1
C37 R87 1
C37 R88 1
C37 R89 1
C37 R90 1
C37 R91 1
C37 R92 1
C37 R93 1
C37 R94 1
C37 R95 1
C37 R96 1
C37 R97 1
C37 R98 1
C37 R99 1
C37 qc0 -1.5167111111111120e+00
C38 R28 1
C38 R29 2
C38 R33 1
C38 R34 2
C38 R38 1
C38 R39 2
C38 R43 1
C38 R44 2
C38 R48 1
C38 R49 2
C38 R78 1
C38 R79 2
C38 R83 1
C38 R84 2
C38 R88 1
C38 R89 2
C38 R93 1
C38 R94 2
C38 R98 1
C38 R99 2
C38 R130 1
C38 R131 1
C38 R132 1
C38 R133 1
C38 R134 1
C38 R135 1
C38 R136 1
C38 R137 1
C38 R138 1
C38 R139 1
C38 qc0 -2.3251259259259274e+00
C39 R29 1
C39 R34 1
C39 R39 1
C39 R44 1
C39 R49 1
C39 R79 1
C39 R84 1
C39 R89 1
C39 R94 1
C39 R99 1
C39 R135 1
C39 R136 1
C39 R137 1
C39 R138 1
C39 R139 1
C39 qc0 -8.5007407407407476e-01
C40 R40 -1
C40 R45 -2
C40 R90 -1
C40 R95 -2
C40 R123 1
C40 R124 2
C41 R40 -2
C41 R41 -1
C41 R45 -4
C41 R46 -2
C41 R90 -2
C41 R91 -1
C41 R95 -4
C41 R96 -2
C41 R123 1
C41 R124 2
C41 R128 1
C41 R129 2
C42 R40 1
C42 R41 1
C42 R42 1
C42 R43 1
C42 R44 1
C42 R45 2
C42 R46 2
C42 R47 2
C42 R48 2
C42 R49 2
C42 R90 1
C42 R91 1
C42 R92 1
C42 R93 1
C42 R94 1
C42 R95 2
C42 R96 2
C42 R97 2
C42 R98 2
C42 R99 2
C42 qc0 -2.3251259259259274e+00
C43 R43 1
C43 R44 2
C43 R48 2
C43 R49 4
C43 R93 1
C43 R94 2
C43 R98 2
C43 R99 4
C43 R133 1
C43 R134 2
C43 R138 1
C43 R139 2
C43 qc0 -3.7836592576790156e+00
C44 R44 1
C44 R49 2
C44 R94 1
C44 R99 2
C44 R138 1
C44 R139 2
C44 qc0 -1.4835259248724297e+00
C45 R45 -1
C45 R95 -1
C45 R124 1
C46 R45 -2
C46 R46 -1
C46 R95 -2
C46 R96 -1
C46 R124 1
C46 R129 1
C47 R45 1
C47 R46 1
C47 R47 1
C47 R48 1
C47 R49 1
C47 R95 1
C47 R96 1
C47 R97 1
C47 R98 1
C47 R99 1
C47 qc0 -8.5007407407407476e-01
C48 R48 1
C48 R49 2
C48 R98 1
C48 R99 2
C48 R134 1
C48 R139 1
C48 qc0 -1.4835259248724297e+00
C49 R49 1
C49 R99 1
C49 R139 1
C49 qc0 -6.3345185079835586e-01
RHS
RHS1 R0 -1.9999999999999911e+00
RHS1 R1 -1.9999999999999911e+00
RHS1 R2 -1.9999999999999911e+00
RHS1 R3 -1.9999999999999911e+00
RHS1 R4 -1.9999999999999911e+00
RHS1 R5 -1.9999999999999911e+00
RHS1 R6 -1.9999999999999911e+00
RHS1 R7 -1.9999999999999911e+00
RHS1 R8 -1.9999999999999911e+00
RHS1 R9 -1.9999999999999911e+00
RHS1 R10 -1.9999999999999911e+00
RHS1 R11 -1.9999999999999911e+00
RHS1 R12 -1.9999999999999911e+00
RHS1 R13 -1.9999999999999911e+00
RHS1 R14 -1.9999999999999911e+00
RHS1 R15 -1.9999999999999911e+00
RHS1 R16 -1.9999999999999911e+00
RHS1 R17 -1.9999999999999911e+00
RHS1 R18 -1.9999999999999911e+00
RHS1 R19 -1.9999999999999911e+00
RHS1 R20 -1.9999999999999911e+00
RHS1 R21 -1.9999999999999911e+00
RHS1 R22 -1.9999999999999911e+00
RHS1 R23 -1.9999999999999911e+00
RHS1 R24 -1.9999999999999911e+00
RHS1 R25 -1.9999999999999911e+00
RHS1 R26 -1.9999999999999911e+00
RHS1 R27 -1.9999999999999911e+00
RHS1 R28 -1.9999999999999911e+00
RHS1 R29 -1.9999999999999911e+00
RHS1 R30 -1.9999999999999911e+00
RHS1 R31 -1.9999999999999911e+00
RHS1 R32 -1.9999999999999911e+00
RHS1 R33 -1.9999999999999911e+00
RHS1 R34 -1.9999999999999911e+00
RHS1 R35 -1.9999999999999911e+00
RHS1 R36 -1.9999999999999911e+00
RHS1 R37 -1.9999999999999911e+00
RHS1 R38 -1.9999999999999911e+00
RHS1 R39 -1.9999999999999911e+00
RHS1 R40 -1.9999999999999911e+00
RHS1 R41 -1.9999999999999911e+00
RHS1 R42 -1.9999999999999911e+00
RHS1 R43 -1.9999999999999911e+00
RHS1 R44 -1.9999999999999911e+00
RHS1 R45 -1.9999999999999911e+00
RHS1 R46 -1.9999999999999911e+00
RHS1 R47 -1.9999999999999911e+00
RHS1 R48 -1.9999999999999911e+00
RHS1 R49 -1.9999999999999911e+00
RHS1 R50 5.0000000000000009e+00
RHS1 R51 5.0000000000000009e+00
RHS1 R52 5.0000000000000009e+00
RHS1 R53 5.0000000000000009e+00
RHS1 R54 5.0000000000000009e+00
RHS1 R55 5.0000000000000009e+00
RHS1 R56 5.0000000000000009e+00
RHS1 R57 5.0000000000000009e+00
RHS1 R58 5.0000000000000009e+00
RHS1 R59 5.0000000000000009e+00
RHS1 R60 5.0000000000000009e+00
RHS1 R61 5.0000000000000009e+00
RHS1 R62 5.0000000000000009e+00
RHS1 R63 5.0000000000000009e+00
RHS1 R64 5.0000000000000009e+00
RHS1 R65 5.0000000000000009e+00
RHS1 R66 5.0000000000000009e+00
RHS1 R67 5.0000000000000009e+00
RHS1 R68 5.0000000000000009e+00
RHS1 R69 5.0000000000000009e+00
RHS1 R70 5.0000000000000009e+00
RHS1 R71 5.0000000000000009e+00
RHS1 R72 5.0000000000000009e+00
RHS1 R73 5.0000000000000009e+00
RHS1 R74 5.0000000000000009e+00
RHS1 R75 5.0000000000000009e+00
RHS1 R76 5.0000000000000009e+00
RHS1 R77 5.0000000000000009e+00
RHS1 R78 5.0000000000000009e+00
RHS1 R79 5.0000000000000009e+00
RHS1 R80 5.0000000000000009e+00
RHS1 R81 5.0000000000000009e+00
RHS1 R82 5.0000000000000009e+00
RHS1 R83 5.0000000000000009e+00
RHS1 R84 5.0000000000000009e+00
RHS1 R85 5.0000000000000009e+00
RHS1 R86 5.0000000000000009e+00
RHS1 R87 5.0000000000000009e+00
RHS1 R88 5.0000000000000009e+00
RHS1 R89 5.0000000000000009e+00
RHS1 R90 5.0000000000000009e+00
RHS1 R91 5.0000000000000009e+00
RHS1 R92 5.0000000000000009e+00
RHS1 R93 5.0000000000000009e+00
RHS1 R94 5.0000000000000009e+00
RHS1 R95 5.0000000000000009e+00
RHS1 R96 5.0000000000000009e+00
RHS1 R97 5.0000000000000009e+00
RHS1 R98 5.0000000000000009e+00
RHS1 R99 5.0000000000000009e+00
RHS1 qc0 -3.3782829337747238e+00
BOUNDS
FR BND1 C0
FR BND1 C1
FR BND1 C2
FR BND1 C3
FR BND1 C4
FR BND1 C5
FR BND1 C6
FR BND1 C7
FR BND1 C8
FR BND1 C9
FR BND1 C10
FR BND1 C11
FR BND1 C12
FR BND1 C13
FR BND1 C14
FR BND1 C15
FR BND1 C16
FR BND1 C17
FR BND1 C18
FR BND1 C19
FR BND1 C20
FR BND1 C21
FR BND1 C22
FR BND1 C23
FR BND1 C24
FR BND1 C25
FR BND1 C26
FR BND1 C27
FR BND1 C28
FR BND1 C29
FR BND1 C30
FR BND1 C31
FR BND1 C32
FR BND1 C33
FR BND1 C34
FR BND1 C35
FR BND1 C36
FR BND1 C37
FR BND1 C38
FR BND1 C39
FR BND1 C40
FR BND1 C41
FR BND1 C42
FR BND1 C43
FR BND1 C44
FR BND1 C45
FR BND1 C46
FR BND1 C47
FR BND1 C48
FR BND1 C49
QCMATRIX qc0
C0 C0 5.1681481218107228e-02
C0 C1 1.1585925899588490e-01
C1 C0 1.1585925899588490e-01
C0 C2 -6.4177777777777667e-02
C2 C0 -6.4177777777777667e-02
C0 C5 1.1585925899588490e-01
C5 C0 1.1585925899588490e-01
C0 C6 0.26504444418107
C6 C0 0.26504444418107
C0 C7 -1.4918518518518509e-01
C7 C0 -1.4918518518518509e-01
C0 C10 -6.4177777777777667e-02
C10 C0 -6.4177777777777667e-02
C0 C11 -1.4918518518518509e-01
C11 C0 -1.4918518518518509e-01
C0 C12 8.5007407407407420e-02
C12 C0 8.5007407407407420e-02
C1 C1 0.26504444418107
C1 C2 -1.4918518518518509e-01
C2 C1 -1.4918518518518509e-01
C1 C5 0.26504444418107
C5 C1 0.26504444418107
C1 C6 6.2590370344032920e-01
C6 C1 6.2590370344032920e-01
C1 C7 -3.6085925925925921e-01
C7 C1 -3.6085925925925921e-01
C1 C10 -1.4918518518518509e-01
C10 C1 -1.4918518518518509e-01
C1 C11 -3.6085925925925921e-01
C11 C1 -3.6085925925925921e-01
C1 C12 2.1167407407407413e-01
C12 C1 2.1167407407407413e-01
C2 C2 8.5007407407407420e-02
C2 C5 -1.4918518518518509e-01
C5 C2 -1.4918518518518509e-01
C2 C6 -3.6085925925925921e-01
C6 C2 -3.6085925925925921e-01
C2 C7 2.1167407407407413e-01
C7 C2 2.1167407407407413e-01
C2 C10 8.5007407407407420e-02
C10 C2 8.5007407407407420e-02
C2 C11 2.1167407407407413e-01
C11 C2 2.1167407407407413e-01
C2 C12 -1.2666666666666671e-01
C12 C2 -1.2666666666666671e-01
C5 C5 0.26504444418107
C5 C6 6.2590370344032920e-01
C6 C5 6.2590370344032920e-01
C5 C7 -3.6085925925925921e-01
C7 C5 -3.6085925925925921e-01
C5 C10 -1.4918518518518509e-01
C10 C5 -1.4918518518518509e-01
C5 C11 -3.6085925925925921e-01
C11 C5 -3.6085925925925921e-01
C5 C12 2.1167407407407413e-01
C12 C5 2.1167407407407413e-01
C6 C6 1.6267851846584362e+00
C6 C7 -1.0133777777777777e+00
C7 C6 -1.0133777777777777e+00
C6 C10 -3.6085925925925921e-01
C10 C6 -3.6085925925925921e-01
C6 C11 -1.0133777777777777e+00
C11 C6 -1.0133777777777777e+00
C6 C12 6.7334814814814825e-01
C12 C6 6.7334814814814825e-01
C7 C7 6.7334814814814825e-01
C7 C10 2.1167407407407413e-01
C10 C7 2.1167407407407413e-01
C7 C11 6.7334814814814825e-01
C11 C7 6.7334814814814825e-01
C7 C12 -5.0333333333333341e-01
C12 C7 -5.0333333333333341e-01
C10 C10 8.5007407407407420e-02
C10 C11 2.1167407407407413e-01
C11 C10 2.1167407407407413e-01
C10 C12 -1.2666666666666671e-01
C12 C10 -1.2666666666666671e-01
C11 C11 6.7334814814814825e-01
C11 C12 -5.0333333333333341e-01
C12 C11 -5.0333333333333341e-01
C12 C12 0.5
C37 C37 0.5
C37 C38 5.0333333333333352e-01
C38 C37 5.0333333333333352e-01
C37 C39 1.2666666666666676e-01
C39 C37 1.2666666666666676e-01
C37 C42 5.0333333333333352e-01
C42 C37 5.0333333333333352e-01
C37 C43 6.7334814814814836e-01
C43 C37 6.7334814814814836e-01
C37 C44 2.1167407407407418e-01
C44 C37 2.1167407407407418e-01
C37 C47 1.2666666666666676e-01
C47 C37 1.2666666666666676e-01
C37 C48 2.1167407407407418e-01
C48 C37 2.1167407407407418e-01
C37 C49 8.5007407407407420e-02
C49 C37 8.5007407407407420e-02
C38 C38 6.7334814814814836e-01
C38 C39 2.1167407407407418e-01
C39 C38 2.1167407407407418e-01
C38 C42 6.7334814814814836e-01
C42 C38 6.7334814814814836e-01
C38 C43 1.0133777777777782e+00
C43 C38 1.0133777777777782e+00
C38 C44 3.6085925925925944e-01
C44 C38 3.6085925925925944e-01
C38 C47 2.1167407407407418e-01
C47 C38 2.1167407407407418e-01
C38 C48 3.6085925925925944e-01
C48 C38 3.6085925925925944e-01
C38 C49 1.4918518518518520e-01
C49 C38 1.4918518518518520e-01
C39 C39 8.5007407407407420e-02
C39 C42 2.1167407407407418e-01
C42 C39 2.1167407407407418e-01
C39 C43 3.6085925925925944e-01
C43 C39 3.6085925925925944e-01
C39 C44 1.4918518518518525e-01
C44 C39 1.4918518518518525e-01
C39 C47 8.5007407407407420e-02
C47 C39 8.5007407407407420e-02
C39 C48 1.4918518518518525e-01
C48 C39 1.4918518518518525e-01
C39 C49 0.0641777777777778
C49 C39 0.0641777777777778
C42 C42 6.7334814814814836e-01
C42 C43 1.0133777777777782e+00
C43 C42 1.0133777777777782e+00
C42 C44 3.6085925925925944e-01
C44 C42 3.6085925925925944e-01
C42 C47 2.1167407407407418e-01
C47 C42 2.1167407407407418e-01
C42 C48 3.6085925925925944e-01
C48 C42 3.6085925925925944e-01
C42 C49 1.4918518518518520e-01
C49 C42 1.4918518518518520e-01
C43 C43 1.6267851846584371e+00
C43 C44 6.2590370344032975e-01
C44 C43 6.2590370344032975e-01
C43 C47 3.6085925925925944e-01
C47 C43 3.6085925925925944e-01
C43 C48 6.2590370344032975e-01
C48 C43 6.2590370344032975e-01
C43 C49 2.6504444418107043e-01
C49 C43 2.6504444418107043e-01
C44 C44 2.6504444418107032e-01
C44 C47 1.4918518518518525e-01
C47 C44 1.4918518518518525e-01
C44 C48 2.6504444418107032e-01
C48 C44 2.6504444418107032e-01
C44 C49 1.1585925899588512e-01
C49 C44 1.1585925899588512e-01
C47 C47 8.5007407407407420e-02
C47 C48 1.4918518518518525e-01
C48 C47 1.4918518518518525e-01
C47 C49 0.0641777777777778
C49 C47 0.0641777777777778
C48 C48 2.6504444418107032e-01
C48 C49 1.1585925899588512e-01
C49 C48 1.1585925899588512e-01
C49 C49 5.1681481218107450e-02
ENDATALarger model (step2_mod.mps)
NAME R
ROWS
N OBJ
G R0
G R1
G R2
G R3
G R4
G R5
G R6
G R7
G R8
G R9
G R10
G R11
G R12
G R13
G R14
G R15
G R16
G R17
G R18
G R19
G R20
G R21
G R22
G R23
G R24
G R25
G R26
G R27
G R28
G R29
G R30
G R31
G R32
G R33
G R34
G R35
G R36
G R37
G R38
G R39
G R40
G R41
G R42
G R43
G R44
G R45
G R46
G R47
G R48
G R49
L R50
L R51
L R52
L R53
L R54
L R55
L R56
L R57
L R58
L R59
L R60
L R61
L R62
L R63
L R64
L R65
L R66
L R67
L R68
L R69
L R70
L R71
L R72
L R73
L R74
L R75
L R76
L R77
L R78
L R79
L R80
L R81
L R82
L R83
L R84
L R85
L R86
L R87
L R88
L R89
L R90
L R91
L R92
L R93
L R94
L R95
L R96
L R97
L R98
L R99
G R100
G R101
G R102
G R103
G R104
G R105
G R106
G R107
G R108
G R109
G R110
G R111
G R112
G R113
G R114
G R115
G R116
G R117
G R118
G R119
G R120
G R121
G R122
G R123
G R124
G R125
G R126
G R127
G R128
G R129
G R130
G R131
G R132
G R133
G R134
G R135
G R136
G R137
G R138
G R139
G R140
L qc0
COLUMNS
C0 R0 1
C0 R50 1
C0 R100 -1
C0 R140 -1
C0 qc0 -2.9342222116872513e-01
C1 R0 2
C1 R1 1
C1 R50 2
C1 R51 1
C1 R100 -1
C1 R105 -1
C1 R140 -2
C1 qc0 -6.3682962857613257e-01
C2 R0 -1
C2 R1 -1
C2 R2 -1
C2 R3 -1
C2 R4 -1
C2 R50 -1
C2 R51 -1
C2 R52 -1
C2 R53 -1
C2 R54 -1
C2 qc0 3.4340740740740738e-01
C3 R3 -1
C3 R4 -2
C3 R53 -1
C3 R54 -2
C3 R110 -1
C3 R115 -1
C4 R4 -1
C4 R54 -1
C4 R115 -1
C5 R0 2
C5 R5 1
C5 R50 2
C5 R55 1
C5 R100 -2
C5 R101 -1
C5 R140 -2
C5 qc0 -6.3682962857613257e-01
C6 R0 4
C6 R1 2
C6 R5 2
C6 R6 1
C6 R50 4
C6 R51 2
C6 R55 2
C6 R56 1
C6 R100 -2
C6 R101 -1
C6 R105 -2
C6 R106 -1
C6 R140 -4
C6 qc0 -1.0902666650864219e+00
C7 R0 -2
C7 R1 -2
C7 R2 -2
C7 R3 -2
C7 R4 -2
C7 R5 -1
C7 R6 -1
C7 R7 -1
C7 R8 -1
C7 R9 -1
C7 R50 -2
C7 R51 -2
C7 R52 -2
C7 R53 -2
C7 R54 -2
C7 R55 -1
C7 R56 -1
C7 R57 -1
C7 R58 -1
C7 R59 -1
C7 qc0 3.1179259259259307e-01
C8 R3 -2
C8 R4 -4
C8 R8 -1
C8 R9 -2
C8 R53 -2
C8 R54 -4
C8 R58 -1
C8 R59 -2
C8 R110 -2
C8 R111 -1
C8 R115 -2
C8 R116 -1
C9 R4 -2
C9 R9 -1
C9 R54 -2
C9 R59 -1
C9 R115 -2
C9 R116 -1
C10 R0 -1
C10 R5 -1
C10 R10 -1
C10 R15 -1
C10 R20 -1
C10 R50 -1
C10 R55 -1
C10 R60 -1
C10 R65 -1
C10 R70 -1
C10 R100 1
C10 R101 1
C10 R102 1
C10 R103 1
C10 R104 1
C10 R140 1
C10 qc0 3.4340740740740738e-01
C11 R0 -2
C11 R1 -1
C11 R5 -2
C11 R6 -1
C11 R10 -2
C11 R11 -1
C11 R15 -2
C11 R16 -1
C11 R20 -2
C11 R21 -1
C11 R50 -2
C11 R51 -1
C11 R55 -2
C11 R56 -1
C11 R60 -2
C11 R61 -1
C11 R65 -2
C11 R66 -1
C11 R70 -2
C11 R71 -1
C11 R100 1
C11 R101 1
C11 R102 1
C11 R103 1
C11 R104 1
C11 R105 1
C11 R106 1
C11 R107 1
C11 R108 1
C11 R109 1
C11 R140 2
C11 qc0 3.1179259259259307e-01
C12 OBJ -1
C12 R0 1
C12 R1 1
C12 R2 1
C12 R3 1
C12 R4 1
C12 R5 1
C12 R6 1
C12 R7 1
C12 R8 1
C12 R9 1
C12 R10 1
C12 R11 1
C12 R12 1
C12 R13 1
C12 R14 1
C12 R15 1
C12 R16 1
C12 R17 1
C12 R18 1
C12 R19 1
C12 R20 1
C12 R21 1
C12 R22 1
C12 R23 1
C12 R24 1
C12 R50 1
C12 R51 1
C12 R52 1
C12 R53 1
C12 R54 1
C12 R55 1
C12 R56 1
C12 R57 1
C12 R58 1
C12 R59 1
C12 R60 1
C12 R61 1
C12 R62 1
C12 R63 1
C12 R64 1
C12 R65 1
C12 R66 1
C12 R67 1
C12 R68 1
C12 R69 1
C12 R70 1
C12 R71 1
C12 R72 1
C12 R73 1
C12 R74 1
C12 qc0 4.8328888888888732e-01
C13 R3 1
C13 R4 2
C13 R8 1
C13 R9 2
C13 R13 1
C13 R14 2
C13 R18 1
C13 R19 2
C13 R23 1
C13 R24 2
C13 R53 1
C13 R54 2
C13 R58 1
C13 R59 2
C13 R63 1
C13 R64 2
C13 R68 1
C13 R69 2
C13 R73 1
C13 R74 2
C13 R110 1
C13 R111 1
C13 R112 1
C13 R113 1
C13 R114 1
C13 R115 1
C13 R116 1
C13 R117 1
C13 R118 1
C13 R119 1
C14 R4 1
C14 R9 1
C14 R14 1
C14 R19 1
C14 R24 1
C14 R54 1
C14 R59 1
C14 R64 1
C14 R69 1
C14 R74 1
C14 R115 1
C14 R116 1
C14 R117 1
C14 R118 1
C14 R119 1
C15 R15 -1
C15 R20 -2
C15 R65 -1
C15 R70 -2
C15 R103 1
C15 R104 2
C16 R15 -2
C16 R16 -1
C16 R20 -4
C16 R21 -2
C16 R65 -2
C16 R66 -1
C16 R70 -4
C16 R71 -2
C16 R103 1
C16 R104 2
C16 R108 1
C16 R109 2
C17 R15 1
C17 R16 1
C17 R17 1
C17 R18 1
C17 R19 1
C17 R20 2
C17 R21 2
C17 R22 2
C17 R23 2
C17 R24 2
C17 R65 1
C17 R66 1
C17 R67 1
C17 R68 1
C17 R69 1
C17 R70 2
C17 R71 2
C17 R72 2
C17 R73 2
C17 R74 2
C18 R18 1
C18 R19 2
C18 R23 2
C18 R24 4
C18 R68 1
C18 R69 2
C18 R73 2
C18 R74 4
C18 R113 1
C18 R114 2
C18 R118 1
C18 R119 2
C19 R19 1
C19 R24 2
C19 R69 1
C19 R74 2
C19 R118 1
C19 R119 2
C20 R20 -1
C20 R70 -1
C20 R104 1
C21 R20 -2
C21 R21 -1
C21 R70 -2
C21 R71 -1
C21 R104 1
C21 R109 1
C22 R20 1
C22 R21 1
C22 R22 1
C22 R23 1
C22 R24 1
C22 R70 1
C22 R71 1
C22 R72 1
C22 R73 1
C22 R74 1
C23 R23 1
C23 R24 2
C23 R73 1
C23 R74 2
C23 R114 1
C23 R119 1
C24 R24 1
C24 R74 1
C24 R119 1
C25 R25 1
C25 R75 1
C25 R120 -1
C26 R25 2
C26 R26 1
C26 R75 2
C26 R76 1
C26 R120 -1
C26 R125 -1
C27 R25 -1
C27 R26 -1
C27 R27 -1
C27 R28 -1
C27 R29 -1
C27 R75 -1
C27 R76 -1
C27 R77 -1
C27 R78 -1
C27 R79 -1
C28 R28 -1
C28 R29 -2
C28 R78 -1
C28 R79 -2
C28 R130 -1
C28 R135 -1
C29 R29 -1
C29 R79 -1
C29 R135 -1
C30 R25 2
C30 R30 1
C30 R75 2
C30 R80 1
C30 R120 -2
C30 R121 -1
C31 R25 4
C31 R26 2
C31 R30 2
C31 R31 1
C31 R75 4
C31 R76 2
C31 R80 2
C31 R81 1
C31 R120 -2
C31 R121 -1
C31 R125 -2
C31 R126 -1
C32 R25 -2
C32 R26 -2
C32 R27 -2
C32 R28 -2
C32 R29 -2
C32 R30 -1
C32 R31 -1
C32 R32 -1
C32 R33 -1
C32 R34 -1
C32 R75 -2
C32 R76 -2
C32 R77 -2
C32 R78 -2
C32 R79 -2
C32 R80 -1
C32 R81 -1
C32 R82 -1
C32 R83 -1
C32 R84 -1
C33 R28 -2
C33 R29 -4
C33 R33 -1
C33 R34 -2
C33 R78 -2
C33 R79 -4
C33 R83 -1
C33 R84 -2
C33 R130 -2
C33 R131 -1
C33 R135 -2
C33 R136 -1
C34 R29 -2
C34 R34 -1
C34 R79 -2
C34 R84 -1
C34 R135 -2
C34 R136 -1
C35 R25 -1
C35 R30 -1
C35 R35 -1
C35 R40 -1
C35 R45 -1
C35 R75 -1
C35 R80 -1
C35 R85 -1
C35 R90 -1
C35 R95 -1
C35 R120 1
C35 R121 1
C35 R122 1
C35 R123 1
C35 R124 1
C36 R25 -2
C36 R26 -1
C36 R30 -2
C36 R31 -1
C36 R35 -2
C36 R36 -1
C36 R40 -2
C36 R41 -1
C36 R45 -2
C36 R46 -1
C36 R75 -2
C36 R76 -1
C36 R80 -2
C36 R81 -1
C36 R85 -2
C36 R86 -1
C36 R90 -2
C36 R91 -1
C36 R95 -2
C36 R96 -1
C36 R120 1
C36 R121 1
C36 R122 1
C36 R123 1
C36 R124 1
C36 R125 1
C36 R126 1
C36 R127 1
C36 R128 1
C36 R129 1
C37 OBJ 1
C37 R25 1
C37 R26 1
C37 R27 1
C37 R28 1
C37 R29 1
C37 R30 1
C37 R31 1
C37 R32 1
C37 R33 1
C37 R34 1
C37 R35 1
C37 R36 1
C37 R37 1
C37 R38 1
C37 R39 1
C37 R40 1
C37 R41 1
C37 R42 1
C37 R43 1
C37 R44 1
C37 R45 1
C37 R46 1
C37 R47 1
C37 R48 1
C37 R49 1
C37 R75 1
C37 R76 1
C37 R77 1
C37 R78 1
C37 R79 1
C37 R80 1
C37 R81 1
C37 R82 1
C37 R83 1
C37 R84 1
C37 R85 1
C37 R86 1
C37 R87 1
C37 R88 1
C37 R89 1
C37 R90 1
C37 R91 1
C37 R92 1
C37 R93 1
C37 R94 1
C37 R95 1
C37 R96 1
C37 R97 1
C37 R98 1
C37 R99 1
C37 qc0 -1.5167111111111120e+00
C38 R28 1
C38 R29 2
C38 R33 1
C38 R34 2
C38 R38 1
C38 R39 2
C38 R43 1
C38 R44 2
C38 R48 1
C38 R49 2
C38 R78 1
C38 R79 2
C38 R83 1
C38 R84 2
C38 R88 1
C38 R89 2
C38 R93 1
C38 R94 2
C38 R98 1
C38 R99 2
C38 R130 1
C38 R131 1
C38 R132 1
C38 R133 1
C38 R134 1
C38 R135 1
C38 R136 1
C38 R137 1
C38 R138 1
C38 R139 1
C38 qc0 -2.3251259259259274e+00
C39 R29 1
C39 R34 1
C39 R39 1
C39 R44 1
C39 R49 1
C39 R79 1
C39 R84 1
C39 R89 1
C39 R94 1
C39 R99 1
C39 R135 1
C39 R136 1
C39 R137 1
C39 R138 1
C39 R139 1
C39 qc0 -8.5007407407407476e-01
C40 R40 -1
C40 R45 -2
C40 R90 -1
C40 R95 -2
C40 R123 1
C40 R124 2
C41 R40 -2
C41 R41 -1
C41 R45 -4
C41 R46 -2
C41 R90 -2
C41 R91 -1
C41 R95 -4
C41 R96 -2
C41 R123 1
C41 R124 2
C41 R128 1
C41 R129 2
C42 R40 1
C42 R41 1
C42 R42 1
C42 R43 1
C42 R44 1
C42 R45 2
C42 R46 2
C42 R47 2
C42 R48 2
C42 R49 2
C42 R90 1
C42 R91 1
C42 R92 1
C42 R93 1
C42 R94 1
C42 R95 2
C42 R96 2
C42 R97 2
C42 R98 2
C42 R99 2
C42 qc0 -2.3251259259259274e+00
C43 R43 1
C43 R44 2
C43 R48 2
C43 R49 4
C43 R93 1
C43 R94 2
C43 R98 2
C43 R99 4
C43 R133 1
C43 R134 2
C43 R138 1
C43 R139 2
C43 qc0 -3.7836592576790156e+00
C44 R44 1
C44 R49 2
C44 R94 1
C44 R99 2
C44 R138 1
C44 R139 2
C44 qc0 -1.4835259248724297e+00
C45 R45 -1
C45 R95 -1
C45 R124 1
C46 R45 -2
C46 R46 -1
C46 R95 -2
C46 R96 -1
C46 R124 1
C46 R129 1
C47 R45 1
C47 R46 1
C47 R47 1
C47 R48 1
C47 R49 1
C47 R95 1
C47 R96 1
C47 R97 1
C47 R98 1
C47 R99 1
C47 qc0 -8.5007407407407476e-01
C48 R48 1
C48 R49 2
C48 R98 1
C48 R99 2
C48 R134 1
C48 R139 1
C48 qc0 -1.4835259248724297e+00
C49 R49 1
C49 R99 1
C49 R139 1
C49 qc0 -6.3345185079835586e-01
RHS
RHS1 R0 -1.9999999999999911e+00
RHS1 R1 -1.9999999999999911e+00
RHS1 R2 -1.9999999999999911e+00
RHS1 R3 -1.9999999999999911e+00
RHS1 R4 -1.9999999999999911e+00
RHS1 R5 -1.9999999999999911e+00
RHS1 R6 -1.9999999999999911e+00
RHS1 R7 -1.9999999999999911e+00
RHS1 R8 -1.9999999999999911e+00
RHS1 R9 -1.9999999999999911e+00
RHS1 R10 -1.9999999999999911e+00
RHS1 R11 -1.9999999999999911e+00
RHS1 R12 -1.9999999999999911e+00
RHS1 R13 -1.9999999999999911e+00
RHS1 R14 -1.9999999999999911e+00
RHS1 R15 -1.9999999999999911e+00
RHS1 R16 -1.9999999999999911e+00
RHS1 R17 -1.9999999999999911e+00
RHS1 R18 -1.9999999999999911e+00
RHS1 R19 -1.9999999999999911e+00
RHS1 R20 -1.9999999999999911e+00
RHS1 R21 -1.9999999999999911e+00
RHS1 R22 -1.9999999999999911e+00
RHS1 R23 -1.9999999999999911e+00
RHS1 R24 -1.9999999999999911e+00
RHS1 R25 -1.9999999999999911e+00
RHS1 R26 -1.9999999999999911e+00
RHS1 R27 -1.9999999999999911e+00
RHS1 R28 -1.9999999999999911e+00
RHS1 R29 -1.9999999999999911e+00
RHS1 R30 -1.9999999999999911e+00
RHS1 R31 -1.9999999999999911e+00
RHS1 R32 -1.9999999999999911e+00
RHS1 R33 -1.9999999999999911e+00
RHS1 R34 -1.9999999999999911e+00
RHS1 R35 -1.9999999999999911e+00
RHS1 R36 -1.9999999999999911e+00
RHS1 R37 -1.9999999999999911e+00
RHS1 R38 -1.9999999999999911e+00
RHS1 R39 -1.9999999999999911e+00
RHS1 R40 -1.9999999999999911e+00
RHS1 R41 -1.9999999999999911e+00
RHS1 R42 -1.9999999999999911e+00
RHS1 R43 -1.9999999999999911e+00
RHS1 R44 -1.9999999999999911e+00
RHS1 R45 -1.9999999999999911e+00
RHS1 R46 -1.9999999999999911e+00
RHS1 R47 -1.9999999999999911e+00
RHS1 R48 -1.9999999999999911e+00
RHS1 R49 -1.9999999999999911e+00
RHS1 R50 5.0000000000000009e+00
RHS1 R51 5.0000000000000009e+00
RHS1 R52 5.0000000000000009e+00
RHS1 R53 5.0000000000000009e+00
RHS1 R54 5.0000000000000009e+00
RHS1 R55 5.0000000000000009e+00
RHS1 R56 5.0000000000000009e+00
RHS1 R57 5.0000000000000009e+00
RHS1 R58 5.0000000000000009e+00
RHS1 R59 5.0000000000000009e+00
RHS1 R60 5.0000000000000009e+00
RHS1 R61 5.0000000000000009e+00
RHS1 R62 5.0000000000000009e+00
RHS1 R63 5.0000000000000009e+00
RHS1 R64 5.0000000000000009e+00
RHS1 R65 5.0000000000000009e+00
RHS1 R66 5.0000000000000009e+00
RHS1 R67 5.0000000000000009e+00
RHS1 R68 5.0000000000000009e+00
RHS1 R69 5.0000000000000009e+00
RHS1 R70 5.0000000000000009e+00
RHS1 R71 5.0000000000000009e+00
RHS1 R72 5.0000000000000009e+00
RHS1 R73 5.0000000000000009e+00
RHS1 R74 5.0000000000000009e+00
RHS1 R75 5.0000000000000009e+00
RHS1 R76 5.0000000000000009e+00
RHS1 R77 5.0000000000000009e+00
RHS1 R78 5.0000000000000009e+00
RHS1 R79 5.0000000000000009e+00
RHS1 R80 5.0000000000000009e+00
RHS1 R81 5.0000000000000009e+00
RHS1 R82 5.0000000000000009e+00
RHS1 R83 5.0000000000000009e+00
RHS1 R84 5.0000000000000009e+00
RHS1 R85 5.0000000000000009e+00
RHS1 R86 5.0000000000000009e+00
RHS1 R87 5.0000000000000009e+00
RHS1 R88 5.0000000000000009e+00
RHS1 R89 5.0000000000000009e+00
RHS1 R90 5.0000000000000009e+00
RHS1 R91 5.0000000000000009e+00
RHS1 R92 5.0000000000000009e+00
RHS1 R93 5.0000000000000009e+00
RHS1 R94 5.0000000000000009e+00
RHS1 R95 5.0000000000000009e+00
RHS1 R96 5.0000000000000009e+00
RHS1 R97 5.0000000000000009e+00
RHS1 R98 5.0000000000000009e+00
RHS1 R99 5.0000000000000009e+00
RHS1 qc0 -3.3782829337747238e+00
BOUNDS
FR BND1 C0
FR BND1 C1
FR BND1 C2
FR BND1 C3
FR BND1 C4
FR BND1 C5
FR BND1 C6
FR BND1 C7
FR BND1 C8
FR BND1 C9
FR BND1 C10
FR BND1 C11
FR BND1 C12
FR BND1 C13
FR BND1 C14
FR BND1 C15
FR BND1 C16
FR BND1 C17
FR BND1 C18
FR BND1 C19
FR BND1 C20
FR BND1 C21
FR BND1 C22
FR BND1 C23
FR BND1 C24
FR BND1 C25
FR BND1 C26
FR BND1 C27
FR BND1 C28
FR BND1 C29
FR BND1 C30
FR BND1 C31
FR BND1 C32
FR BND1 C33
FR BND1 C34
FR BND1 C35
FR BND1 C36
FR BND1 C37
FR BND1 C38
FR BND1 C39
FR BND1 C40
FR BND1 C41
FR BND1 C42
FR BND1 C43
FR BND1 C44
FR BND1 C45
FR BND1 C46
FR BND1 C47
FR BND1 C48
FR BND1 C49
QCMATRIX qc0
C0 C0 5.1681481218107228e-02
C0 C1 1.1585925899588490e-01
C1 C0 1.1585925899588490e-01
C0 C2 -6.4177777777777667e-02
C2 C0 -6.4177777777777667e-02
C0 C5 1.1585925899588490e-01
C5 C0 1.1585925899588490e-01
C0 C6 0.26504444418107
C6 C0 0.26504444418107
C0 C7 -1.4918518518518509e-01
C7 C0 -1.4918518518518509e-01
C0 C10 -6.4177777777777667e-02
C10 C0 -6.4177777777777667e-02
C0 C11 -1.4918518518518509e-01
C11 C0 -1.4918518518518509e-01
C0 C12 8.5007407407407420e-02
C12 C0 8.5007407407407420e-02
C1 C1 0.26504444418107
C1 C2 -1.4918518518518509e-01
C2 C1 -1.4918518518518509e-01
C1 C5 0.26504444418107
C5 C1 0.26504444418107
C1 C6 6.2590370344032920e-01
C6 C1 6.2590370344032920e-01
C1 C7 -3.6085925925925921e-01
C7 C1 -3.6085925925925921e-01
C1 C10 -1.4918518518518509e-01
C10 C1 -1.4918518518518509e-01
C1 C11 -3.6085925925925921e-01
C11 C1 -3.6085925925925921e-01
C1 C12 2.1167407407407413e-01
C12 C1 2.1167407407407413e-01
C2 C2 8.5007407407407420e-02
C2 C5 -1.4918518518518509e-01
C5 C2 -1.4918518518518509e-01
C2 C6 -3.6085925925925921e-01
C6 C2 -3.6085925925925921e-01
C2 C7 2.1167407407407413e-01
C7 C2 2.1167407407407413e-01
C2 C10 8.5007407407407420e-02
C10 C2 8.5007407407407420e-02
C2 C11 2.1167407407407413e-01
C11 C2 2.1167407407407413e-01
C2 C12 -1.2666666666666671e-01
C12 C2 -1.2666666666666671e-01
C5 C5 0.26504444418107
C5 C6 6.2590370344032920e-01
C6 C5 6.2590370344032920e-01
C5 C7 -3.6085925925925921e-01
C7 C5 -3.6085925925925921e-01
C5 C10 -1.4918518518518509e-01
C10 C5 -1.4918518518518509e-01
C5 C11 -3.6085925925925921e-01
C11 C5 -3.6085925925925921e-01
C5 C12 2.1167407407407413e-01
C12 C5 2.1167407407407413e-01
C6 C6 1.6267851846584362e+00
C6 C7 -1.0133777777777777e+00
C7 C6 -1.0133777777777777e+00
C6 C10 -3.6085925925925921e-01
C10 C6 -3.6085925925925921e-01
C6 C11 -1.0133777777777777e+00
C11 C6 -1.0133777777777777e+00
C6 C12 6.7334814814814825e-01
C12 C6 6.7334814814814825e-01
C7 C7 6.7334814814814825e-01
C7 C10 2.1167407407407413e-01
C10 C7 2.1167407407407413e-01
C7 C11 6.7334814814814825e-01
C11 C7 6.7334814814814825e-01
C7 C12 -5.0333333333333341e-01
C12 C7 -5.0333333333333341e-01
C10 C10 8.5007407407407420e-02
C10 C11 2.1167407407407413e-01
C11 C10 2.1167407407407413e-01
C10 C12 -1.2666666666666671e-01
C12 C10 -1.2666666666666671e-01
C11 C11 6.7334814814814825e-01
C11 C12 -5.0333333333333341e-01
C12 C11 -5.0333333333333341e-01
C12 C12 0.5
C37 C37 0.5
C37 C38 5.0333333333333352e-01
C38 C37 5.0333333333333352e-01
C37 C39 1.2666666666666676e-01
C39 C37 1.2666666666666676e-01
C37 C42 5.0333333333333352e-01
C42 C37 5.0333333333333352e-01
C37 C43 6.7334814814814836e-01
C43 C37 6.7334814814814836e-01
C37 C44 2.1167407407407418e-01
C44 C37 2.1167407407407418e-01
C37 C47 1.2666666666666676e-01
C47 C37 1.2666666666666676e-01
C37 C48 2.1167407407407418e-01
C48 C37 2.1167407407407418e-01
C37 C49 8.5007407407407420e-02
C49 C37 8.5007407407407420e-02
C38 C38 6.7334814814814836e-01
C38 C39 2.1167407407407418e-01
C39 C38 2.1167407407407418e-01
C38 C42 6.7334814814814836e-01
C42 C38 6.7334814814814836e-01
C38 C43 1.0133777777777782e+00
C43 C38 1.0133777777777782e+00
C38 C44 3.6085925925925944e-01
C44 C38 3.6085925925925944e-01
C38 C47 2.1167407407407418e-01
C47 C38 2.1167407407407418e-01
C38 C48 3.6085925925925944e-01
C48 C38 3.6085925925925944e-01
C38 C49 1.4918518518518520e-01
C49 C38 1.4918518518518520e-01
C39 C39 8.5007407407407420e-02
C39 C42 2.1167407407407418e-01
C42 C39 2.1167407407407418e-01
C39 C43 3.6085925925925944e-01
C43 C39 3.6085925925925944e-01
C39 C44 1.4918518518518525e-01
C44 C39 1.4918518518518525e-01
C39 C47 8.5007407407407420e-02
C47 C39 8.5007407407407420e-02
C39 C48 1.4918518518518525e-01
C48 C39 1.4918518518518525e-01
C39 C49 0.0641777777777778
C49 C39 0.0641777777777778
C42 C42 6.7334814814814836e-01
C42 C43 1.0133777777777782e+00
C43 C42 1.0133777777777782e+00
C42 C44 3.6085925925925944e-01
C44 C42 3.6085925925925944e-01
C42 C47 2.1167407407407418e-01
C47 C42 2.1167407407407418e-01
C42 C48 3.6085925925925944e-01
C48 C42 3.6085925925925944e-01
C42 C49 1.4918518518518520e-01
C49 C42 1.4918518518518520e-01
C43 C43 1.6267851846584371e+00
C43 C44 6.2590370344032975e-01
C44 C43 6.2590370344032975e-01
C43 C47 3.6085925925925944e-01
C47 C43 3.6085925925925944e-01
C43 C48 6.2590370344032975e-01
C48 C43 6.2590370344032975e-01
C43 C49 2.6504444418107043e-01
C49 C43 2.6504444418107043e-01
C44 C44 2.6504444418107032e-01
C44 C47 1.4918518518518525e-01
C47 C44 1.4918518518518525e-01
C44 C48 2.6504444418107032e-01
C48 C44 2.6504444418107032e-01
C44 C49 1.1585925899588512e-01
C49 C44 1.1585925899588512e-01
C47 C47 8.5007407407407420e-02
C47 C48 1.4918518518518525e-01
C48 C47 1.4918518518518525e-01
C47 C49 0.0641777777777778
C49 C47 0.0641777777777778
C48 C48 2.6504444418107032e-01
C48 C49 1.1585925899588512e-01
C49 C48 1.1585925899588512e-01
C49 C49 5.1681481218107450e-02
ENDATA
Comparison of mps files
0 -
Hello Simon,
In case it helps, I also uploaded the mps files in my previous post to a Dropbox. Rather than copy-pasting these files from above, you can download them using the links below:
- Smaller model (step2_minimal.mps) -- https://www.dropbox.com/s/9xwfvpxmc4awzk3/step2_minimal.mps?dl=0
- Larger model (step2_mod.mps) -- https://www.dropbox.com/s/d8rba548vn4qodm/step2_mod.mps?dl=0
If you'd like to see the lp and log files from my original post, please use this link: https://www.dropbox.com/sh/6cnr9j7fdchid0a/AAAwzZQjw3NJ86fGNyWCQ3KUa?dl=0
Thanks for looking into this. Hope to hear from you soon.
0 -
Hello,
Since my last post, I have reformulated the quadratic constraint so that it is more sparse. For example, instead of expanding
|| Qx - b ||^2 < c
to write our quadratic constraint, we instead expand
|| z ||^2 < c
where z is a new auxiliary variable that is equal to Qx - b.
This reformulation dramatically improves the accuracy of our results. Now, the final solution to the program is the same with and without this redundant constraint. The presolve procedure also removes a lot more rows under the reformulation. However, the redundant constraint still isn't eliminated during the presolve procedure.
Do you know why reformulating the quadratic constraint has such a big impact on the presolve procedure and on the final program altogether?
If you're interested in seeing the lp and log files using the reformulation, please use this link: https://www.dropbox.com/sh/3x6nlgtc92pixwn/AADvtZwfAsrDjLYqdAhqsNCra?dl=0. This link also contains the lp and log files using the original version of the quadratic constraint.
0
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