Gurobi QP 求解器以不稳定的方式工作

如何解决Gurobi QP 求解器以不稳定的方式工作

我遇到了 QP 求解器工作不稳定的问题。我在每次迭代中都用相同的结构解决 QP 问题。目标函数是相同的二次项，每次迭代我都会向模型添加一个额外的约束。在前 23 次迭代中，QP 求解器工作正常。然而，QP 求解器在一些迭代后突然需要更多的时间来求解。

例如在第 23 次迭代时，日志如下：

Gurobi Optimizer version 9.1.1 build v9.1.1rc0 (mac64)
Thread count: 8 physical cores,16 logical processors,using up to 16 threads
Optimize a model with 164054 rows,107382 columns and 1338753 nonzeros
Model fingerprint: 0xc2fda6a2
Model has 1876 quadratic objective terms
Coefficient statistics:
Matrix range [3e-08,9e+04]
Objective range [4e-11,2e+01]
QObjective range [7e-02,2e+00]
Bounds range [6e-01,3e+05]
RHS range [1e-01,2e+05]
Warning: Model contains large matrix coefficient range
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 109551 rows and 60994 columns
Presolve time: 0.45s
Presolved: 54503 rows,46388 columns,789446 nonzeros
Presolved model has 1876 quadratic objective terms
Ordering time: 0.53s
Ordering time: 1.20s

Barrier statistics:
Dense cols : 62
AA' NZ : 1.796e+06
Factor NZ : 1.611e+07 (roughly 170 MBytes of memory)
Factor Ops : 6.055e+09 (less than 1 second per iteration)
Threads : 8

Objective Residual
Iter Primal Dual Primal Dual Compl Time
0 6.48426994e+13 -1.95781010e+14 3.53e+07 2.39e+05 7.83e+10 2s
1 2.30780707e+13 -1.48965948e+14 1.91e+07 1.30e+05 4.56e+10 2s
2 9.17891136e+12 -1.33874808e+14 1.15e+07 7.82e+04 3.07e+10 2s
3 7.91137041e+11 -1.10030794e+14 3.51e+06 2.38e+04 1.15e+10 3s
4 2.17837548e+11 -8.89072421e+13 1.93e+06 1.31e+04 6.78e+09 3s
5 6.03769303e+10 -7.85266738e+13 1.04e+06 7.03e+03 4.37e+09 3s
6 3.61265994e+09 -4.91634200e+13 2.42e+05 1.64e+03 1.36e+09 3s
7 1.22959900e+09 -3.84134934e+13 1.33e+05 9.01e+02 9.15e+08 3s
8 6.77854454e+08 -3.02708227e+13 9.64e+04 6.54e+02 7.27e+08 3s
9 2.54139180e+08 -2.18700152e+13 5.69e+04 3.86e+02 5.12e+08 3s
10 1.67321977e+08 -1.87392597e+13 4.53e+04 3.08e+02 4.32e+08 4s
11 6.48426994e+13 -1.95781010e+14 3.53e+07 2.39e+05 7.83e+10 4s
12 2.99831742e+11 -3.34320097e+12 2.22e+06 1.51e+04 5.52e+08 4s
13 2.43309692e+10 -8.10105087e+11 5.90e+05 3.93e+03 6.64e+07 4s
14 1.54235357e+09 -1.78797505e+11 1.41e+05 9.36e+02 7.90e+06 4s
15 2.23435394e+08 -6.80312249e+10 5.36e+04 3.57e+02 2.24e+06 4s
16 1.05231586e+08 -4.58000748e+10 3.61e+04 2.40e+02 1.35e+06 4s
17 5.33354313e+07 -3.08732269e+10 2.43e+04 1.62e+02 8.34e+05 5s
18 2.23223875e+07 -1.88637387e+10 1.48e+04 9.88e+01 4.80e+05 5s
19 2.37706916e+06 -4.87406691e+09 3.84e+03 2.56e+01 1.08e+05 5s
20 1.24593691e+06 -3.39225923e+09 2.67e+03 1.78e+01 6.95e+04 5s
21 4.55461665e+05 -1.86016525e+09 1.46e+03 9.74e+00 3.34e+04 5s
22 2.75024024e+05 -1.34176297e+09 1.06e+03 7.03e+00 2.26e+04 5s
23 1.52878349e+05 -9.07675288e+08 7.13e+02 4.75e+00 1.40e+04 6s
24 8.06500345e+04 -5.56255713e+08 4.37e+02 2.91e+00 7.81e+03 6s
25 5.77189648e+04 -4.10229971e+08 3.22e+02 2.15e+00 5.48e+03 6s
26 5.16328832e+04 -3.66510614e+08 2.88e+02 1.92e+00 4.82e+03 6s
27 3.47356116e+04 -2.36157205e+08 1.85e+02 1.23e+00 2.95e+03 6s
28 3.01151007e+04 -1.90166354e+08 1.49e+02 9.94e-01 2.31e+03 6s
29 2.23818033e+04 -1.10377007e+08 8.66e+01 5.77e-01 1.27e+03 7s
30 1.85170060e+04 -6.42490949e+07 5.04e+01 3.36e-01 7.12e+02 7s
31 1.71181663e+04 -4.73409797e+07 3.72e+01 2.47e-01 5.15e+02 7s
32 1.49475469e+04 -1.68368396e+07 1.32e+01 8.79e-02 1.76e+02 7s
33 1.31215513e+04 -2.05208999e+06 1.61e+00 1.07e-02 2.11e+01 7s
34 1.00292399e+04 -2.76420971e+05 2.27e-01 1.51e-03 2.91e+00 7s
35 8.53543189e+03 -1.95526428e+05 1.64e-01 1.09e-03 2.08e+00 7s
36 8.17136737e+03 -1.72343632e+05 1.46e-01 9.69e-04 1.84e+00 8s
37 7.89546501e+03 -1.60723517e+05 1.36e-01 9.08e-04 1.71e+00 8s
38 7.02957960e+03 -1.32061015e+05 1.14e-01 7.57e-04 1.41e+00 8s
39 6.36319538e+03 -1.12625997e+05 9.83e-02 6.54e-04 1.21e+00 8s
40 5.94751134e+03 -1.01019910e+05 8.90e-02 5.92e-04 1.09e+00 8s
41 4.89409241e+03 -8.14138282e+04 7.26e-02 4.83e-04 8.77e-01 8s
42 4.82765154e+03 -7.95756578e+04 7.11e-02 4.73e-04 8.57e-01 8s
43 4.49253510e+03 -7.09301469e+04 6.40e-02 4.26e-04 7.66e-01 9s
44 4.06926048e+03 -6.20694963e+04 5.67e-02 3.77e-04 6.72e-01 9s
45 2.91914045e+03 -3.86666099e+04 3.70e-02 2.46e-04 4.22e-01 9s
46 2.33954512e+03 -2.79061760e+04 2.75e-02 1.83e-04 3.07e-01 9s
47 1.73989926e+03 -1.77681331e+04 1.83e-02 1.22e-04 1.98e-01 9s
48 1.10610644e+03 -1.06390454e+04 1.17e-02 7.76e-05 1.19e-01 9s
49 8.24671446e+02 -7.44495159e+03 8.67e-03 5.77e-05 8.38e-02 10s
50 5.15422456e+02 -4.64783175e+03 5.67e-03 3.78e-05 5.23e-02 10s
51 2.97241338e+02 -2.69311150e+03 3.49e-03 2.32e-05 3.02e-02 10s
52 1.98086373e+02 -1.85105945e+03 2.47e-03 1.64e-05 2.07e-02 10s
53 1.41178629e+02 -1.38133525e+03 1.87e-03 1.25e-05 1.54e-02 10s
54 8.30805446e+01 -8.87014487e+02 1.22e-03 8.15e-06 9.79e-03 10s
55 5.47577519e+01 -5.98521969e+02 8.85e-04 5.89e-06 6.59e-03 10s
56 3.78199633e+01 -4.51993998e+02 6.48e-04 4.31e-06 4.94e-03 11s
57 2.85885779e+01 -3.84966836e+02 4.79e-04 3.19e-06 4.16e-03 11s
58 2.27839752e+01 -3.12861197e+02 4.00e-04 2.66e-06 3.37e-03 11s
59 1.63470815e+01 -2.37402301e+02 2.75e-04 1.83e-06 2.55e-03 11s
60 1.22887280e+01 -1.86459669e+02 2.07e-04 1.37e-06 1.99e-03 11s
61 1.11098501e+01 -1.70371677e+02 1.87e-04 1.24e-06 1.82e-03 11s
62 8.93789330e+00 -1.38729998e+02 1.44e-04 9.61e-07 1.48e-03 12s
63 7.41122958e+00 -1.16533131e+02 1.11e-04 7.39e-07 1.24e-03 12s
64 6.93434914e+00 -1.09336253e+02 1.05e-04 6.96e-07 1.16e-03 12s
65 6.78537877e+00 -1.07037751e+02 1.02e-04 6.82e-07 1.14e-03 12s
66 5.82949231e+00 -9.23652800e+01 8.46e-05 5.63e-07 9.82e-04 12s
67 5.06515293e+00 -7.95160040e+01 7.09e-05 4.72e-07 8.45e-04 12s
68 4.61638871e+00 -7.16159092e+01 6.42e-05 4.27e-07 7.62e-04 12s
69 4.13202163e+00 -6.43020115e+01 5.57e-05 3.71e-07 6.84e-04 13s
70 2.60266838e+00 -3.96274408e+01 3.23e-05 2.15e-07 4.22e-04 13s
71 2.22283189e+00 -3.37367968e+01 2.31e-05 1.54e-07 3.59e-04 13s
72 1.65543347e+00 -2.41542930e+01 1.13e-05 7.50e-08 2.57e-04 13s
73 1.36468987e+00 -1.81225617e+01 7.85e-06 5.22e-08 1.94e-04 13s
74 1.23950929e+00 -1.58639935e+01 6.56e-06 4.37e-08 1.70e-04 13s
75 1.00016329e+00 -1.12424539e+01 3.43e-06 2.28e-08 1.22e-04 14s
76 7.94250834e-01 -6.83743613e+00 1.30e-06 8.68e-09 7.57e-05 14s
77 6.07205738e-01 -2.83440051e+00 2.09e-07 1.39e-09 3.41e-05 14s
78 6.03943103e-01 -2.75740497e+00 1.89e-07 1.26e-09 3.33e-05 14s
79 5.56924660e-01 -9.73106797e-01 6.70e-09 4.46e-11 1.52e-05 14s
80 5.17702916e-01 -6.88815374e-02 4.10e-10 2.67e-12 5.81e-06 14s
81 5.05706078e-01 4.30962307e-01 1.94e-11 1.98e-13 7.41e-07 15s
82 5.04461712e-01 4.86505491e-01 2.12e-11 4.20e-14 1.78e-07 15s
83 5.04083134e-01 5.03659707e-01 9.16e-12 7.91e-16 4.20e-09 15s
84 5.04074193e-01 5.04073703e-01 2.08e-11 1.58e-15 4.85e-12 15s

Barrier solved model in 84 iterations and 15.15 seconds
Optimal objective 5.04074193e-01


User-callback calls 36246,time in user-callback 0.07 sec

然而，当我在第 24 次迭代时，它是：

Gurobi Optimizer version 9.1.1 build v9.1.1rc0 (mac64)
Thread count: 8 physical cores,using up to 16 threads
Optimize a model with 164810 rows,107382 columns and 1376563 nonzeros
Model fingerprint: 0xd65e127c
Model has 1876 quadratic objective terms
Coefficient statistics:
Matrix range [3e-08,2e+05]
Warning: Model contains large matrix coefficient range
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Presolve removed 109633 rows and 60916 columns
Presolve time: 0.46s
Presolved: 55177 rows,46466 columns,818354 nonzeros
Presolved model has 1876 quadratic objective terms
Ordering time: 0.65s
Elapsed ordering time = 5s
Elapsed ordering time = 6s
Elapsed ordering time = 8s
Elapsed ordering time = 10s
Elapsed ordering time = 10s
Ordering time: 11.01s

Barrier statistics:
AA' NZ : 3.933e+07
Factor NZ : 7.830e+08 (roughly 6.0 GBytes of memory)
Factor Ops : 1.651e+13 (roughly 70 seconds per iteration)
Threads : 8

Objective Residual
Iter Primal Dual Primal Dual Compl Time
0 6.63854293e+13 -1.94541185e+14 3.55e+07 2.42e+05 7.75e+10 120s
1 1.44911927e+13 -1.37385643e+14 1.50e+07 1.02e+05 3.47e+10 228s

如您所见，我停止了求解器，因为很明显在第 24 次迭代时发生了一些不同的事情，并使 QP 表现不佳。

谁能告诉我如何解决这个问题？

非常感谢！