Я выполнил свое решение на Cplex и получил результат ниже. Наконец, он провел много итераций с символом звезды (*). Я напечатал статус решения = 6. Означает ли это, что моя проблема не может достичь оптимальной, и переменные, которые я получил, не могут быть точными?Cplex дает статус решения = 6, это значит, что у моей проблемы нет обходного решения?
Tried aggregator 1 time.
QP Presolve eliminated 1070 rows and 7712 columns.
Aggregator did 1 substitutions.
Reduced QP has 19229 rows, 11762 columns, and 70837 nonzeros.
Reduced QP objective Q matrix has 9999 nonzeros.
Presolve time = 0.06 sec. (15.71 ticks)
Parallel mode: using up to 4 threads for barrier.
***NOTE: Found 185 dense columns.
Number of nonzeros in lower triangle of A*A' = 237322
Using Nested Dissection ordering
Total time for automatic ordering = 0.51 sec. (186.51 ticks)
Summary statistics for Cholesky factor:
Threads = 4
Rows in Factor = 19414
Integer space required = 84705
Total non-zeros in factor = 1315542
Total FP ops to factor = 377093574
Itn Primal Obj Dual Obj Prim Inf Upper Inf Dual Inf
0 2.1556826e+024 -2.1556826e+024 2.90e+016 0.00e+000 4.15e+012
1 2.8969373e+022 -2.8969375e+022 3.37e+015 0.00e+000 4.82e+011
2 6.6438243e+021 -6.6438260e+021 1.61e+015 0.00e+000 2.31e+011
3 1.5738876e+021 -1.5738892e+021 7.85e+014 0.00e+000 1.12e+011
4 8.7363163e+020 -8.7363321e+020 5.85e+014 0.00e+000 8.36e+010
5 5.6810167e+020 -5.6810318e+020 4.72e+014 0.00e+000 6.74e+010
6 1.3407969e+020 -1.3408088e+020 2.29e+014 0.00e+000 3.28e+010
7 2.6178239e+019 -2.6178999e+019 1.01e+014 0.00e+000 1.45e+010
8 1.5196152e+018 -1.5199449e+018 2.43e+013 0.00e+000 3.48e+009
9 1.8788865e+016 -1.8834049e+016 2.61e+012 0.00e+000 3.73e+008
10 1.1565062e+015 -1.1745630e+015 5.17e+011 0.00e+000 7.39e+007
11 1.8402445e+014 -1.9572763e+014 5.36e+010 0.00e+000 7.67e+006
12 2.3338839e+013 -3.9167399e+013 6.84e-001 0.00e+000 3.16e+003
13 -2.0461928e+013 -1.0305044e+013 2.72e-001 0.00e+000 1.81e+003
14 -8.5727163e+013 -2.7114059e+012 1.92e-001 0.00e+000 9.54e+002
15 -1.2863131e+014 -4.3393850e+011 1.74e-001 0.00e+000 1.69e+003
16 -3.3998821e+014 -6.2601017e+010 2.44e-001 0.00e+000 1.63e+002
17 -4.8972995e+014 -8.9929658e+009 3.81e-001 0.00e+000 8.95e+001
18 -8.0163587e+014 -1.2980223e+009 3.85e-001 0.00e+000 3.06e+001
19 -9.9926360e+014 -1.9645121e+008 8.59e-002 0.00e+000 2.50e+001
20 -2.3645253e+015 -3.3591755e+007 1.85e-001 0.00e+000 1.81e+001
21 -2.3645489e+015 -3.6655103e+007 3.93e-001 0.00e+000 1.82e+001
22 -2.3665146e+015 -4.2775757e+007 3.87e-001 0.00e+000 1.80e+001
23 -2.4122749e+015 -5.0062938e+007 5.21e-001 0.00e+000 1.76e+001
24 -2.5774166e+015 -1.0009577e+007 1.46e+000 0.00e+000 1.88e+001
25 -2.5830270e+015 -1.6715236e+007 1.81e+000 0.00e+000 1.87e+001
26 -3.2012216e+015 -5.6710775e+006 5.38e-001 0.00e+000 1.75e+001
27 -7.5080027e+015 -1.9991081e+006 1.72e+000 0.00e+000 1.74e+001
28 -1.4664526e+016 -9.4070118e+005 9.55e-001 0.00e+000 1.74e+001
29 -1.4671054e+016 -2.3754747e+006 5.81e+000 0.00e+000 1.74e+001
30 -1.4675288e+016 -5.8554481e+006 4.72e+000 0.00e+000 1.75e+001
31 -1.4688208e+016 -1.5933011e+007 4.63e+000 0.00e+000 1.75e+001
32 -1.4820493e+016 -5.0999417e+007 5.64e+000 0.00e+000 1.76e+001
33 -1.8009464e+016 -1.0809049e+007 4.77e+000 0.00e+000 1.74e+001
34 -2.1147351e+016 -1.5196820e+007 5.82e+001 0.00e+000 1.74e+001
35 -3.1087060e+016 -4.1509264e+006 1.79e+001 0.00e+000 1.74e+001
36 -4.6998748e+016 -1.5490984e+006 6.66e+000 0.00e+000 1.74e+001
37 -6.6410451e+016 -9.0730197e+005 1.00e+001 0.00e+000 1.73e+001
38 -6.6412915e+016 -1.2692245e+006 2.97e+001 0.00e+000 1.74e+001
39 -6.6421938e+016 -2.3703454e+006 2.11e+001 0.00e+000 1.74e+001
40 -6.6467293e+016 -7.3051760e+006 5.57e+001 0.00e+000 1.74e+001
41 -6.6608951e+016 -1.9147451e+007 3.27e+001 0.00e+000 1.75e+001
42 -6.7172366e+016 -6.3713529e+007 2.44e+001 0.00e+000 1.75e+001
43 -6.8996611e+016 -1.6047844e+008 3.13e+001 0.00e+000 1.74e+001
44 -7.5224067e+016 -2.9844653e+008 2.22e+001 0.00e+000 1.74e+001
45 -8.8541981e+016 -2.9298621e+008 1.93e+001 0.00e+000 1.72e+001
46 -1.5484919e+017 -7.7191292e+009 1.99e+001 0.00e+000 1.68e+001
47 -2.4846059e+017 -2.0001282e+009 4.10e+001 0.00e+000 1.67e+001
48 -2.9179330e+017 -3.4143835e+009 6.96e+001 0.00e+000 1.81e+001
49 -3.0331831e+017 -8.6988051e+009 6.82e+001 0.00e+000 1.79e+001
50 -5.0822921e+017 -5.3511719e+009 9.99e+001 0.00e+000 1.61e+001
51 -8.7831029e+017 -1.1762106e+009 2.51e+001 0.00e+000 1.62e+001
52 -1.2006404e+018 -6.0523067e+009 1.75e+002 0.00e+000 1.87e+001
* -2.5774166e+015 -1.0009577e+007 1.46e+000 0.00e+000 1.88e+001
Barrier time = 5.75 sec. (1675.34 ticks)
Total time on 4 threads = 5.75 sec. (1675.34 ticks)
Solution status = 6 :
Решатель имеет численные трудности. Поэтому прочтите [this] (http://www.ibm.com/support/knowledgecenter/SSSA5P_12.2.0/ilog.odms.cplex.help/Content/Optimization/Documentation/CPLEX/_pubskel/CPLEX429.html) и [это] (https://www.tu-chemnitz.de/mathematik/discrete/manuals/cplex/doc/userman/html/solveLPS33.html). Вероятно, есть много вариантов настройки. – sascha