Why do I encounter numerical issues when solving the model?
回答済み
I encountered numerical issues while running a second-order cone optimization model, but the model's coefficient statistics seem fine. I have set 'NumericFocus' to 3 and 'BarHomogeneous' to 1, yet I still receive numerical error messages. The model's .lp file is available in the following OneDrive link. I would like to know what could be causing the numerical issues and if there are any methods to resolve them. Thank you.
https://1drv.ms/u/c/f3004033f0c5eb61/EZlJZJ8UzjNHlUstAwCYLOoBi7bSOnMdpKeYgnTquBV5UA?e=dlBqw0
Coefficient statistics:
Matrix range [2e-03, 2e+03]
QMatrix range [2e-02, 1e+00]
Objective range [5e+00, 1e+02]
QObjective range [2e+01, 2e+01]
Bounds range [9e-01, 3e+02]
RHS range [2e-02, 4e+00]
Presolve removed 5357 rows and 57288 columns
Presolve time: 0.04s
Presolved: 18164 rows, 18712 columns, 150527 nonzeros
Presolved model has 759 second-order cone constraints
Ordering time: 0.03s
Barrier statistics:
Dense cols : 240
AA' NZ : 2.675e+05
Factor NZ : 4.483e+05 (roughly 20 MB of memory)
Factor Ops : 3.490e+07 (less than 1 second per iteration)
Threads : 24
Objective Residual
Iter Primal Dual Primal Dual Compl Time
0 -8.07577122e+07 -4.38508651e+09 2.26e+04 1.01e+03 1.12e+06 1s
1 -7.55413966e+06 -8.02496193e+08 5.58e+03 1.27e+02 2.44e+05 2s
2 7.14821147e+06 -1.12758286e+08 6.97e+02 1.57e+01 3.09e+04 3s
3 2.23357952e+06 -2.09071340e+07 1.23e+02 1.97e+00 5.34e+03 4s
4 6.71832281e+05 -7.07297576e+06 3.54e+01 2.15e-01 1.44e+03 6s
5 2.43867359e+05 -3.17186972e+06 1.19e+01 2.34e-02 4.46e+02 7s
6 1.38853003e+05 -1.74646405e+06 6.31e+00 8.15e-03 2.09e+02 9s
7 8.17163803e+04 -9.25154567e+05 3.53e+00 2.73e-03 1.01e+02 11s
8 5.99971992e+04 -6.97641062e+05 2.47e+00 1.79e-03 6.99e+01 14s
9 4.30142708e+04 -3.57525112e+05 1.59e+00 6.87e-04 3.83e+01 20s
10 3.29229636e+04 -2.09635431e+05 1.11e+00 3.85e-04 2.45e+01 24s
11 2.80772838e+04 -1.45318370e+05 8.72e-01 2.68e-04 1.84e+01 27s
12 1.70943578e+04 -3.59663059e+04 3.17e-01 8.18e-05 7.04e+00 31s
13 1.31854299e+04 5.73365624e+03 1.40e-01 3.68e-05 3.43e+00 34s
14 1.12825378e+04 3.07082517e+04 5.99e-02 1.39e-05 1.42e+00 36s
15 1.06067008e+04 3.47898400e+04 3.45e-02 1.02e-05 9.94e-01 38s
16 1.03103572e+04 4.26274592e+04 2.06e-02 3.39e-06 4.75e-01 41s
17 1.00602807e+04 4.63474508e+04 8.43e-03 8.49e-07 1.75e-01 43s
18 9.95936740e+03 4.71035123e+04 5.94e-03 4.66e-07 8.79e-02 45s
19 9.90175533e+03 4.76055142e+04 6.09e-03 2.65e-07 5.03e-02 47s
20 9.81898583e+03 4.80408786e+04 6.37e-03 9.04e-08 2.07e-02 49s
21 9.82249574e+03 4.81299625e+04 6.32e-03 7.79e-08 1.91e-02 51s
22 9.79761351e+03 4.83871705e+04 6.23e-03 5.64e-08 1.58e-02 53s
23 9.74244315e+03 4.84450767e+04 6.16e-03 3.67e-08 1.22e-02 55s
24 9.74682215e+03 4.85429555e+04 6.03e-03 2.51e-08 9.84e-03 56s
25 9.74585467e+03 4.85928178e+04 5.19e-03 2.38e-08 9.06e-03 58s
26 9.78393084e+03 4.87463704e+04 5.38e-03 1.26e-08 6.40e-03 62s
27 9.82364219e+03 4.87714982e+04 5.51e-03 1.16e-08 5.59e-03 63s
28 9.81595011e+03 4.88405241e+04 5.11e-03 8.69e-09 5.33e-03 65s
29 9.80535240e+03 4.88659067e+04 5.09e-03 7.00e-09 5.06e-03 67s
30 9.83565078e+03 4.89878911e+04 1.01e-02 2.99e-09 2.79e-03 68s
31 9.75649567e+03 4.89995175e+04 1.20e-02 2.73e-09 2.34e-03 70s
32 9.77085245e+03 4.90288847e+04 9.04e-03 1.60e-09 1.78e-03 71s
33 9.76818307e+03 4.90496847e+04 8.51e-03 2.07e-09 1.90e-03 73s
34 9.76325243e+03 4.90778022e+04 7.35e-03 2.63e-09 1.49e-03 74s
35 9.74581511e+03 4.90731221e+04 6.57e-03 4.64e-09 1.02e-03 77s
36 9.76673392e+03 4.90744243e+04 3.60e-02 3.82e-09 1.10e-03 78s
37 9.79719297e+03 4.90756333e+04 2.68e-02 4.31e-09 8.70e-04 80s
38 9.79781084e+03 4.90846457e+04 2.54e-02 5.26e-09 8.90e-04 82s
39 9.79550178e+03 4.90945887e+04 2.42e-02 5.61e-09 8.31e-04 84s
40 9.77275024e+03 4.90960834e+04 2.30e-02 7.61e-09 8.91e-04 86s
41 9.77410788e+03 4.90959821e+04 2.30e-02 7.62e-09 8.88e-04 87s
42 9.78027702e+03 4.91019538e+04 2.19e-02 7.43e-09 8.41e-04 89s
43 9.71762305e+03 4.90956599e+04 1.54e-02 1.10e-08 5.88e-04 90s
44 9.70713928e+03 4.90955900e+04 1.51e-02 1.11e-08 5.82e-04 92s
45 9.70733838e+03 4.90991792e+04 1.03e-02 1.93e-08 3.93e-04 93s
46 9.71977586e+03 4.90979994e+04 9.60e-03 2.18e-08 3.76e-04 95s
47 9.71294483e+03 4.90994827e+04 9.39e-03 2.42e-08 3.72e-04 96s
48 9.73639599e+03 4.90993931e+04 9.40e-03 2.42e-08 3.67e-04 97s
49 9.74866287e+03 4.91087029e+04 8.83e-03 1.41e-08 3.47e-04 99s
50 9.75648541e+03 4.91053041e+04 7.64e-03 1.82e-08 2.89e-04 101s
51 9.70872308e+03 4.91026741e+04 6.12e-03 2.29e-08 2.03e-04 103s
52 9.72801118e+03 4.91009398e+04 7.21e-03 3.15e-08 1.52e-04 105s
53 9.71127570e+03 4.91013693e+04 5.08e-03 5.33e-08 1.06e-04 106s
54 9.70685824e+03 4.91395212e+04 5.01e-03 7.21e-08 1.23e-04 108s
55 9.71530459e+03 4.91410062e+04 4.86e-03 1.08e-07 1.09e-04 110s
56 9.70575849e+03 4.91410794e+04 1.22e-02 1.08e-07 1.09e-04 111s
57 9.70438687e+03 4.91414475e+04 1.20e-02 1.04e-07 1.07e-04 112s
58 9.69802573e+03 4.91433667e+04 1.20e-02 1.04e-07 1.05e-04 114s
59 9.68391150e+03 4.91424486e+04 1.22e-02 1.35e-07 9.36e-05 115s
60 9.69287521e+03 4.91519546e+04 1.23e-02 1.32e-07 1.02e-04 117s
61 9.70760581e+03 4.91517299e+04 1.15e-02 1.35e-07 9.23e-05 119s
62 9.73528384e+03 4.91496363e+04 1.84e-02 1.55e-07 1.02e-04 121s
63 9.70859676e+03 4.91470959e+04 1.62e-02 1.63e-07 1.27e-04 122s
Barrier performed 63 iterations in 122.27 seconds (34.51 work units)
Numerical trouble encountered
Model may be infeasible or unbounded. Consider using the
homogeneous algorithm (through parameter 'BarHomogeneous')
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What Gurobi version did you use? Do you use any non-default parameter settings (apart from NumericFocus and BarHomogeneous)?
I tested the model with Version 10 and 11 and default settings and get:Model is infeasible or unbounded
Setting DualReductions=0, the result is infeasible.
Gurobi also computes an IIS with 9 constraints. See How do I use 'compute IIS' to find a subset of constraints that are causing model infeasibility?0 -
Thank you very much for your reply. Since the model can be solved after slightly relaxing the right-hand side of the constraints, does this indicate that the reason for the "Numerical trouble encountered" message is likely due to the model being infeasible?
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I'm not sure what you mean. As I mentioned, I cannot reproduce the numerical error with the model you shared. If you see a numerical error but can solve your model without any problems if you change some right-hand sides, it could be that the model before was infeasible. At least, it was not possible to find a feasible solution.
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