Sub-optimal termination for SOCP problem
I tried to solve a SOCP problem using Gurobi 8.0.1. I set the time-limit to be 1 hour, BarConvTol to be 1e-6, BarQCPConvTol to be 1e-6. I am expecting the algorithm stops either when it reaches the tolerance or reaches the time-limit, while Gurobi stops with a sub-optimal termination at 176 seconds. Could you kindly explain why the algorithm stops at the sub-optimal termination? What is the stopping rule for the SOCP LP problem? How can I change the stopping rule to avoid the algorithm stops with a sub-optimal solution before reaching the time-limit? Thanks.
Optimize a model with 188460 rows, 123146 columns and 616132 nonzeros
Model has 36761 quadratic constraints
Coefficient statistics:
Matrix range [1e+00, 4e+02]
QMatrix range [1e+00, 9e+00]
Objective range [1e+00, 1e+03]
Bounds range [1e+00, 1e+00]
RHS range [1e+00, 5e+03]
Presolve removed 40047 rows and 39439 columns
Presolve time: 0.50s
Presolved: 258696 rows, 157229 columns, 721589 nonzeros
Presolved model has 36761 second-order cone constraints
Ordering time: 0.00s
Barrier statistics:
AA' NZ : 1.213e+07
Factor NZ : 1.505e+07 (roughly 300 MBytes of memory)
Factor Ops : 1.294e+09 (less than 1 second per iteration)
Threads : 4
Objective Residual
Iter Primal Dual Primal Dual Compl Time
0 2.53983640e+08 1.42478989e+05 4.91e+04 1.58e+02 3.90e+04 3s
1 9.46596022e+07 -3.90365150e+07 1.58e+04 2.20e+01 1.15e+04 3s
2 2.53259580e+07 -3.84647475e+07 1.23e+03 1.10e+00 1.00e+03 3s
3 1.57639318e+07 -2.43811518e+07 5.28e+02 4.10e-01 4.37e+02 4s
4 1.28420395e+07 -1.91979011e+07 3.72e+02 2.91e-01 3.11e+02 4s
5 1.13193066e+07 -1.43697767e+07 2.92e+02 2.09e-01 2.41e+02 5s
6 1.08637322e+07 -1.11258174e+07 2.65e+02 1.65e-01 2.12e+02 5s
7 1.07352462e+07 -9.54095757e+06 2.59e+02 1.46e-01 2.02e+02 5s
8 1.03067538e+07 -6.96538452e+06 2.34e+02 1.26e-01 1.82e+02 6s
9 9.48024493e+06 -4.11539999e+06 1.71e+02 1.01e-01 1.37e+02 7s
10 9.48335096e+06 -3.43992492e+05 1.42e+02 7.71e-02 1.13e+02 7s
11 9.14112953e+06 2.58768745e+06 1.13e+02 6.17e-02 8.99e+01 7s
12 9.14556275e+06 5.09289953e+06 9.99e+01 5.25e-02 7.91e+01 8s
13 9.32537143e+06 6.93741598e+06 8.51e+01 4.66e-02 6.80e+01 8s
14 9.56844457e+06 7.91680381e+06 7.94e+01 4.41e-02 6.41e+01 9s
15 1.00007839e+07 8.75182249e+06 7.03e+01 4.17e-02 5.78e+01 9s
16 1.02174435e+07 1.00338154e+07 6.69e+01 3.82e-02 5.46e+01 10s
17 1.03443743e+07 1.17006735e+07 6.46e+01 3.46e-02 5.24e+01 10s
18 1.08236909e+07 1.23006177e+07 5.75e+01 3.34e-02 4.76e+01 11s
19 1.13485996e+07 1.31497636e+07 5.38e+01 3.19e-02 4.52e+01 11s
20 1.16489204e+07 1.48593410e+07 5.06e+01 2.94e-02 4.29e+01 11s
21 1.25849765e+07 1.65580032e+07 4.48e+01 2.72e-02 3.93e+01 12s
22 1.30640881e+07 1.84492921e+07 4.15e+01 2.47e-02 3.65e+01 12s
23 1.35624831e+07 1.87855434e+07 3.87e+01 2.43e-02 3.44e+01 13s
24 1.40376809e+07 2.02697666e+07 3.68e+01 2.30e-02 3.32e+01 13s
25 1.43764492e+07 2.14735488e+07 3.52e+01 2.19e-02 3.22e+01 14s
26 1.52829684e+07 2.23732871e+07 3.15e+01 2.10e-02 2.89e+01 14s
27 1.54547361e+07 2.30965872e+07 3.09e+01 2.04e-02 2.82e+01 14s
28 1.57626984e+07 2.36263060e+07 2.99e+01 1.99e-02 2.73e+01 15s
29 1.59859528e+07 2.42388988e+07 2.92e+01 1.96e-02 2.69e+01 15s
30 1.63730225e+07 2.52292163e+07 2.83e+01 1.89e-02 2.63e+01 16s
31 1.68249705e+07 2.58416033e+07 2.70e+01 1.83e-02 2.52e+01 16s
32 1.72888526e+07 2.63894198e+07 2.60e+01 1.78e-02 2.46e+01 17s
33 1.78050129e+07 2.63465795e+07 2.50e+01 1.75e-02 2.41e+01 17s
34 1.79809381e+07 2.72414452e+07 2.46e+01 1.70e-02 2.39e+01 18s
35 1.82417714e+07 2.79426243e+07 2.40e+01 1.64e-02 2.33e+01 18s
36 1.86621638e+07 2.90705669e+07 2.31e+01 1.57e-02 2.22e+01 18s
37 1.90296138e+07 3.00037072e+07 2.23e+01 1.50e-02 2.14e+01 19s
38 1.94235968e+07 3.09154279e+07 2.18e+01 1.44e-02 2.11e+01 19s
39 1.97926555e+07 3.17919050e+07 2.11e+01 1.37e-02 2.07e+01 20s
40 2.02379410e+07 3.22385094e+07 2.04e+01 1.34e-02 2.00e+01 20s
41 2.08039336e+07 3.28758813e+07 1.95e+01 1.30e-02 1.95e+01 21s
42 2.12617288e+07 3.36570244e+07 1.88e+01 1.26e-02 1.88e+01 21s
43 2.18107777e+07 3.40293589e+07 1.80e+01 1.24e-02 1.81e+01 22s
44 2.19464623e+07 3.46254875e+07 1.78e+01 1.20e-02 1.78e+01 22s
45 2.24487396e+07 3.48623340e+07 1.73e+01 1.19e-02 1.75e+01 23s
46 2.29149072e+07 3.54827632e+07 1.68e+01 1.15e-02 1.72e+01 23s
47 2.32940642e+07 3.61726449e+07 1.63e+01 1.13e-02 1.70e+01 24s
48 2.36036744e+07 3.63071035e+07 1.59e+01 1.12e-02 1.67e+01 24s
49 2.39958779e+07 3.69462219e+07 1.55e+01 1.09e-02 1.61e+01 25s
50 2.42617836e+07 3.71468514e+07 1.52e+01 1.07e-02 1.59e+01 25s
51 2.44949720e+07 3.78644751e+07 1.49e+01 1.03e-02 1.59e+01 26s
52 2.48569095e+07 3.85018216e+07 1.46e+01 9.99e-03 1.58e+01 26s
53 2.56906593e+07 3.93951738e+07 1.40e+01 9.44e-03 1.58e+01 27s
54 2.60381244e+07 3.97990328e+07 1.37e+01 9.18e-03 1.54e+01 27s
55 2.64161636e+07 4.04719898e+07 1.34e+01 8.75e-03 1.53e+01 28s
56 2.66289238e+07 4.09984219e+07 1.32e+01 8.41e-03 1.50e+01 28s
57 2.77769812e+07 4.13680151e+07 1.24e+01 8.19e-03 1.47e+01 29s
58 2.86479191e+07 4.22362364e+07 1.17e+01 7.65e-03 1.41e+01 29s
59 2.90233719e+07 4.33640804e+07 1.14e+01 6.99e-03 1.36e+01 29s
60 2.95227166e+07 4.42976651e+07 1.11e+01 6.45e-03 1.29e+01 30s
61 3.04099352e+07 4.44815279e+07 1.04e+01 6.32e-03 1.23e+01 30s
62 3.10188597e+07 4.48299029e+07 9.98e+00 6.14e-03 1.18e+01 31s
63 3.22134588e+07 4.55456038e+07 9.28e+00 6.36e-03 1.17e+01 31s
64 3.27277018e+07 4.63824337e+07 8.97e+00 6.09e-03 1.16e+01 32s
65 3.31800849e+07 4.68055639e+07 8.73e+00 5.88e-03 1.14e+01 32s
66 3.33521087e+07 4.69169074e+07 8.63e+00 5.82e-03 1.13e+01 33s
67 3.34570863e+07 4.70964276e+07 8.58e+00 5.72e-03 1.12e+01 33s
68 3.41844047e+07 4.76285596e+07 8.14e+00 5.43e-03 1.06e+01 34s
69 3.44877046e+07 4.79726086e+07 7.99e+00 5.18e-03 1.04e+01 34s
70 3.53846553e+07 4.81742303e+07 7.48e+00 5.07e-03 9.82e+00 35s
71 3.60465200e+07 4.84490466e+07 7.16e+00 4.90e-03 9.59e+00 35s
72 3.61858969e+07 4.86004547e+07 7.09e+00 4.78e-03 9.49e+00 36s
73 3.64587968e+07 4.87619503e+07 6.94e+00 4.66e-03 9.28e+00 36s
74 3.65201128e+07 4.88634259e+07 6.91e+00 4.58e-03 9.20e+00 36s
75 3.65967165e+07 4.90799221e+07 6.87e+00 4.43e-03 9.09e+00 37s
76 3.69911526e+07 4.92753610e+07 6.67e+00 5.73e-03 8.89e+00 37s
77 3.76365088e+07 4.95297570e+07 6.34e+00 8.82e-03 8.51e+00 38s
78 3.81938198e+07 4.96423969e+07 6.06e+00 1.30e-02 8.25e+00 38s
79 3.87504292e+07 4.97672105e+07 5.79e+00 2.26e-02 8.03e+00 39s
80 3.90835733e+07 4.98074491e+07 5.63e+00 2.70e-02 7.92e+00 39s
81 3.93429462e+07 5.00102891e+07 5.51e+00 2.80e-02 7.72e+00 39s
82 3.99162332e+07 5.01828681e+07 5.24e+00 4.53e-02 7.52e+00 40s
83 4.00938909e+07 5.05012068e+07 5.16e+00 7.00e-02 7.41e+00 41s
84 4.04867835e+07 5.07813888e+07 4.98e+00 7.21e-02 7.30e+00 41s
85 4.08066044e+07 5.08777570e+07 4.84e+00 7.17e-02 7.14e+00 42s
86 4.10838753e+07 5.11172227e+07 4.72e+00 6.98e-02 6.95e+00 43s
87 4.12178202e+07 5.12194505e+07 4.66e+00 6.90e-02 6.87e+00 43s
88 4.15611945e+07 5.13455499e+07 4.52e+00 6.79e-02 6.71e+00 44s
89 4.16678329e+07 5.14767693e+07 4.48e+00 6.68e-02 6.62e+00 44s
90 4.17307515e+07 5.15390082e+07 4.45e+00 6.63e-02 6.58e+00 45s
91 4.19173328e+07 5.18630211e+07 4.38e+00 6.39e-02 6.41e+00 46s
92 4.24047304e+07 5.21571306e+07 4.21e+00 6.17e-02 6.32e+00 46s
93 4.27300750e+07 5.23797035e+07 4.08e+00 6.01e-02 6.20e+00 47s
94 4.30385582e+07 5.29071527e+07 3.98e+00 5.70e-02 6.31e+00 47s
95 4.33957906e+07 5.31935028e+07 3.85e+00 5.56e-02 6.18e+00 48s
96 4.36089911e+07 5.33017296e+07 3.77e+00 5.45e-02 6.13e+00 49s
97 4.43738436e+07 5.37721280e+07 3.54e+00 5.17e-02 6.36e+00 49s
98 4.47131009e+07 5.39108307e+07 3.43e+00 5.55e-02 6.29e+00 50s
99 4.52963855e+07 5.42905268e+07 3.23e+00 5.27e-02 5.92e+00 50s
100 4.55195074e+07 5.44568297e+07 3.16e+00 5.15e-02 5.79e+00 51s
101 4.59819195e+07 5.48418539e+07 3.03e+00 4.87e-02 5.93e+00 51s
102 4.62586359e+07 5.51861345e+07 2.95e+00 4.62e-02 5.79e+00 53s
103 4.66850193e+07 5.53962868e+07 2.84e+00 4.44e-02 5.86e+00 53s
104 4.69104693e+07 5.55512001e+07 2.77e+00 4.31e-02 5.71e+00 53s
105 4.72238479e+07 5.57388848e+07 2.68e+00 4.15e-02 5.51e+00 54s
106 4.75589961e+07 5.58759362e+07 2.58e+00 4.03e-02 5.42e+00 54s
107 4.80283012e+07 5.61301331e+07 2.44e+00 3.81e-02 5.30e+00 55s
108 4.83406649e+07 5.63476425e+07 2.36e+00 3.64e-02 5.19e+00 55s
109 4.87892684e+07 5.65504460e+07 2.25e+00 3.50e-02 5.11e+00 56s
110 4.92580892e+07 5.67939077e+07 2.13e+00 3.31e-02 4.95e+00 56s
111 4.95745425e+07 5.70358424e+07 2.05e+00 3.10e-02 4.72e+00 57s
112 4.97269868e+07 5.71402622e+07 2.01e+00 3.00e-02 4.62e+00 57s
113 5.00060160e+07 5.72611354e+07 1.94e+00 2.90e-02 4.46e+00 57s
114 5.04099281e+07 5.74473257e+07 1.85e+00 2.72e-02 4.34e+00 58s
115 5.07676252e+07 5.77468495e+07 1.76e+00 2.43e-02 4.25e+00 58s
116 5.12270465e+07 5.78908054e+07 1.66e+00 2.77e-02 4.20e+00 60s
117 5.14167318e+07 5.80490289e+07 1.62e+00 2.59e-02 4.15e+00 60s
118 5.17620687e+07 5.81286100e+07 1.55e+00 2.50e-02 4.12e+00 61s
119 5.19246557e+07 5.82404575e+07 1.51e+00 2.61e-02 3.99e+00 61s
120 5.21480244e+07 5.83350199e+07 1.46e+00 2.84e-02 3.85e+00 62s
121 5.23783361e+07 5.84027504e+07 1.41e+00 3.01e-02 3.72e+00 63s
122 5.25732839e+07 5.85124441e+07 1.36e+00 3.29e-02 3.59e+00 63s
123 5.27108849e+07 5.85490672e+07 1.33e+00 3.38e-02 3.51e+00 64s
124 5.28801498e+07 5.85988077e+07 1.30e+00 3.48e-02 3.42e+00 64s
125 5.30800120e+07 5.86761087e+07 1.26e+00 3.67e-02 3.35e+00 65s
126 5.35334215e+07 5.87431502e+07 1.16e+00 4.73e-02 3.17e+00 65s
127 5.39281248e+07 5.88119739e+07 1.08e+00 5.59e-02 3.12e+00 65s
128 5.40851279e+07 5.88992506e+07 1.05e+00 6.03e-02 3.01e+00 66s
129 5.43796485e+07 5.89578923e+07 9.93e-01 6.88e-02 2.93e+00 66s
130 5.47141908e+07 5.90632863e+07 9.34e-01 8.45e-02 2.97e+00 68s
131 5.49126547e+07 5.91155200e+07 8.95e-01 8.01e-02 2.91e+00 68s
132 5.53307595e+07 5.91990026e+07 8.17e-01 7.06e-02 2.79e+00 69s
133 5.55051265e+07 5.92398197e+07 7.85e-01 6.46e-01 2.73e+00 71s
134 5.56419995e+07 5.92729896e+07 7.57e-01 6.27e-01 2.64e+00 72s
135 5.60627289e+07 5.93228219e+07 6.77e-01 5.82e-01 2.47e+00 74s
136 5.63109405e+07 5.93658106e+07 6.31e-01 5.41e-01 2.37e+00 74s
137 5.68088815e+07 5.94444826e+07 5.41e-01 4.63e-01 2.13e+00 75s
138 5.71106497e+07 5.95374450e+07 4.86e-01 3.88e-01 1.90e+00 78s
139 5.73357221e+07 5.95753483e+07 4.43e-01 3.49e-01 1.74e+00 80s
140 5.77350063e+07 5.96225568e+07 3.74e-01 2.94e-01 1.47e+00 82s
141 5.79404486e+07 5.96430331e+07 3.36e-01 2.64e-01 1.32e+00 83s
142 5.81131048e+07 5.96634573e+07 3.04e-01 2.22e-01 1.21e+00 85s
143 5.82493244e+07 5.96737953e+07 2.79e-01 2.07e-01 1.11e+00 87s
144 5.86483319e+07 5.96998532e+07 9.78e-01 1.61e-01 8.43e-01 89s
145 5.86596235e+07 5.97014130e+07 9.63e-01 1.31e+00 8.28e-01 91s
146 5.86878264e+07 5.97041142e+07 9.40e-01 1.34e+00 8.09e-01 92s
147 5.87208820e+07 5.97095498e+07 9.10e-01 1.26e+00 7.79e-01 93s
148 5.88168048e+07 5.97125174e+07 8.27e-01 4.35e+00 7.20e-01 95s
149 5.88156185e+07 5.97125786e+07 8.26e-01 4.52e+00 7.18e-01 97s
150 5.88405836e+07 5.97137411e+07 2.57e+00 6.60e+00 7.06e-01 98s
151 5.88455609e+07 5.97141805e+07 2.56e+00 6.56e+00 7.02e-01 100s
152 5.89501321e+07 5.97251640e+07 2.28e+00 5.59e+00 6.15e-01 101s
153 5.89516304e+07 5.97251771e+07 2.28e+00 5.59e+00 6.15e-01 104s
154 5.89991341e+07 5.97263433e+07 2.13e+00 5.48e+00 5.81e-01 105s
155 5.90265052e+07 5.97314505e+07 2.05e+00 4.99e+00 5.52e-01 106s
156 5.90945364e+07 5.97346031e+07 3.69e+00 4.54e+00 5.18e-01 109s
157 5.90949938e+07 5.97347131e+07 3.69e+00 4.53e+00 5.17e-01 110s
158 5.91062559e+07 5.97355574e+07 3.63e+00 4.46e+00 5.08e-01 111s
159 5.91191728e+07 5.97356953e+07 3.55e+00 4.44e+00 4.99e-01 112s
160 5.91272805e+07 5.97358534e+07 3.49e+00 4.43e+00 4.92e-01 114s
161 5.91426747e+07 5.97364858e+07 3.40e+00 4.37e+00 4.81e-01 115s
162 5.92555498e+07 5.97435201e+07 2.79e+00 3.68e+00 4.06e-01 118s
163 5.92859257e+07 5.97455653e+07 2.66e+00 3.49e+00 3.86e-01 119s
164 5.93024094e+07 5.97461147e+07 2.59e+00 3.42e+00 3.75e-01 120s
165 5.93889165e+07 5.97495428e+07 2.11e+00 3.08e+00 3.15e-01 121s
166 5.94097443e+07 5.97522587e+07 1.96e+00 2.77e+00 2.90e-01 122s
167 5.94308655e+07 5.97530019e+07 1.83e+00 2.69e+00 2.77e-01 124s
168 5.94444014e+07 5.97553631e+07 1.73e+00 2.43e+00 2.59e-01 126s
169 5.94555390e+07 5.97558807e+07 1.68e+00 2.37e+00 2.52e-01 128s
170 5.94622616e+07 5.97575327e+07 1.65e+00 2.23e+00 2.45e-01 129s
171 5.94787002e+07 5.97577155e+07 1.55e+00 2.21e+00 2.32e-01 130s
172 5.94791383e+07 5.97577127e+07 1.55e+00 2.21e+00 2.32e-01 131s
173 5.94833296e+07 5.97585342e+07 1.54e+00 2.12e+00 2.28e-01 133s
174 5.94865788e+07 5.97590807e+07 1.50e+00 2.04e+00 2.23e-01 134s
175 5.95390738e+07 5.97624092e+07 1.19e+00 1.62e+00 1.78e-01 136s
176 5.95418826e+07 5.97624992e+07 1.18e+00 1.61e+00 1.76e-01 138s
177 5.95475821e+07 5.97632763e+07 1.13e+00 1.51e+00 1.69e-01 139s
178 5.95484259e+07 5.97633611e+07 1.11e+00 1.49e+00 1.67e-01 140s
179 5.95721831e+07 5.97639629e+07 9.84e-01 3.09e+00 1.51e-01 142s
180 5.96189021e+07 5.97663956e+07 7.27e-01 2.39e+00 1.14e-01 143s
181 5.96321565e+07 5.97669270e+07 6.88e-01 2.23e+00 1.07e-01 144s
182 5.96417989e+07 5.97673720e+07 6.11e-01 2.12e+00 9.73e-02 146s
183 5.96450345e+07 5.97675882e+07 5.95e-01 2.09e+00 9.47e-02 147s
184 5.96451925e+07 5.97675922e+07 5.95e-01 2.09e+00 9.47e-02 148s
185 5.96487150e+07 5.97687195e+07 5.68e-01 2.61e+00 8.75e-02 150s
186 5.96510096e+07 5.97690354e+07 5.39e-01 2.16e+02 8.19e-02 151s
187 5.96635395e+07 5.97697391e+07 5.10e-01 1.95e+02 7.61e-02 152s
188 5.96702833e+07 5.97703302e+07 4.56e-01 2.01e+02 6.68e-02 153s
189 5.96727564e+07 5.97705445e+07 4.43e-01 1.93e+02 6.46e-02 155s
190 5.96735613e+07 5.97706416e+07 4.33e-01 1.88e+02 6.30e-02 156s
191 5.96744773e+07 5.97705068e+07 4.24e-01 1.83e+02 6.18e-02 157s
192 5.96749998e+07 5.97705140e+07 4.03e-01 3.28e+02 5.91e-02 158s
193 5.96709591e+07 5.97705090e+07 7.61e-01 3.26e+02 5.86e-02 159s
194 5.96705826e+07 5.97705081e+07 7.61e-01 3.26e+02 5.86e-02 161s
195 5.96707499e+07 5.97705135e+07 7.59e-01 3.25e+02 5.84e-02 162s
196 5.96743170e+07 5.97709262e+07 6.92e-01 3.21e+02 5.41e-02 163s
197 5.96814480e+07 5.97709939e+07 6.18e-01 3.16e+02 4.95e-02 165s
198 5.96819540e+07 5.97712055e+07 5.70e-01 3.00e+02 4.65e-02 166s
199 5.96812206e+07 5.97711484e+07 5.57e-01 2.92e+02 4.61e-02 169s
200 5.96818870e+07 5.97713306e+07 5.43e-01 2.79e+02 4.47e-02 171s
201 5.96821575e+07 5.97713298e+07 5.43e-01 2.79e+02 4.47e-02 172s
202 5.96846941e+07 5.97717386e+07 4.82e-01 2.55e+02 4.06e-02 174s
203 5.96852289e+07 5.97717854e+07 4.63e-01 2.48e+02 3.90e-02 175s
204 5.97238603e+07 5.97717857e+07 3.91e+00 2.48e+02 1.69e-01 176s
Barrier performed 204 iterations in 176.16 seconds
Sub-optimal termination - objective 5.87208820e+07
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