Need a help with the suboptimal solution obtained with the barrier-method ?

Hi there,

I am using Gurobi as the solver to solve a QCP problem and here is an extract from the log file.

Academic license - for non-commercial use only
Optimize a model with 100 rows, 92 columns and 386 nonzeros
Model has 8 quadratic constraints
Coefficient statistics:
Matrix range [1e-03, 2e+00]
QMatrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [0e+00, 0e+00]
RHS range [2e-03, 8e+02]
Presolve removed 12 rows and 0 columns
Presolve time: 0.00s
Presolved: 88 rows, 92 columns, 368 nonzeros
Presolved model has 8 second-order cone constraints
Ordering time: 0.00s

Barrier statistics:
Dense cols : 3
AA' NZ : 8.160e+02
Factor NZ : 9.100e+02
Factor Ops : 1.015e+04 (less than 1 second per iteration)
Threads : 1

Objective Residual
Iter Primal Dual Primal Dual Compl Time
0 -8.46577998e+02 -1.57437522e+03 1.05e+02 4.15e-01 1.38e+01 0s
1 -1.39949798e+03 -1.52859693e+03 1.88e+01 2.43e-02 2.16e+00 0s
2 -1.32423063e+03 -1.30922833e+03 6.92e+00 2.06e-03 9.52e-01 0s
3 -1.15782307e+03 -1.18788049e+03 6.37e+00 5.76e-09 2.11e+00 0s
4 -9.64425722e+02 -1.01413752e+03 3.87e+00 7.64e-11 2.97e+00 0s
5 -8.02374350e+02 -6.82516543e+02 2.13e+00 1.74e-11 2.31e+00 0s
6 -3.63752087e+02 -4.49477966e+02 5.71e-01 2.49e-10 4.00e+00 0s
7 1.02164374e+02 -1.82160585e+02 8.95e-07 1.55e-09 4.66e+00 0s
8 1.62852330e+01 -3.98582461e+01 4.05e-08 7.68e-10 6.19e-01 0s
9 1.39947843e+00 -1.07112348e+00 1.29e-08 1.59e-08 2.62e-02 0s
10 6.30790779e-01 3.93874941e-01 1.72e-07 6.80e-07 2.52e-03 0s
11 6.69621595e-01 5.60940610e-01 6.44e-06 4.04e-07 1.13e-03 0s
12 5.93039123e-01 5.93053159e-01 3.21e-04 1.52e-03 1.68e-04 0s
13 6.01396622e-01 6.01519689e-01 4.49e-05 1.40e-03 1.33e-05 0s
14 6.01670379e-01 6.01672936e-01 1.82e-02 3.40e-01 1.20e-06 0s
15 6.01683230e-01 6.01685441e-01 2.08e-02 1.56e+00 2.61e-07 0s
16 6.01697308e-01 6.01698105e-01 2.99e-02 6.95e-01 3.70e-09 0s
17 6.00736660e-01 6.01203234e-01 4.80e-01 9.44e+01 1.03e-08 0s
18 6.01153212e-01 6.01197384e-01 5.99e-01 3.53e+01 6.48e-09 0s
19 6.01117675e-01 6.01189894e-01 1.42e+01 3.50e+01 1.07e-07 0s
20 6.01156410e-01 6.01235258e-01 1.42e+01 3.50e+01 1.06e-07 0s
21 6.01156479e-01 6.01235336e-01 1.44e+01 3.50e+01 1.06e-07 0s
22 6.00191182e-01 6.01013148e-01 3.65e+00 3.05e+01 5.37e-08 0s
23 6.01007675e-01 6.01013358e-01 3.05e+00 3.97e+00 8.56e-10 0s
24 6.01012274e-01 6.01012278e-01 4.81e+00 4.01e+02 1.40e-11 0s
25 6.01012716e-01 6.01012279e-01 5.57e+02 7.29e+02 1.25e-09 0s
26 6.01012632e-01 6.01012206e-01 5.50e+02 2.63e+03 1.37e-07 0s
27 6.01012628e-01 6.01012199e-01 5.46e+02 2.87e+03 1.42e-07 0s
28 6.01012578e-01 6.01012198e-01 1.43e+03 2.89e+03 1.35e-07 0s
29 6.01012553e-01 6.01012193e-01 1.27e+03 6.12e+03 2.41e-07 0s
30 6.01012534e-01 6.01012181e-01 7.45e+03 7.00e+03 6.16e-08 0s
31 6.01005237e-01 6.01011301e-01 1.30e+05 8.01e+03 6.23e-07 0s
32 6.01005626e-01 6.01041132e-01 1.19e+05 2.67e+05 1.01e-05 0s
33 6.01001439e-01 6.01002121e-01 1.06e+05 2.46e+06 4.75e-05 0s
34 6.00992379e-01 6.00203239e-01 5.83e+04 3.22e+07 5.64e-04 0s
35 6.00838757e-01 5.99549769e-01 3.20e+04 1.42e+08 2.20e-03 0s
36 5.99297000e-01 5.99512160e-01 1.75e+04 7.81e+07 2.34e-02 0s
37 5.99261491e-01 5.99512068e-01 1.75e+04 7.81e+07 2.34e-02 0s
38 5.99010339e-01 5.99484381e-01 1.75e+04 7.82e+07 2.31e-02 0s
39 5.83341766e-01 5.93684192e-01 1.69e+04 1.03e+08 3.23e-03 0s
40 6.13252349e-01 5.99673749e-01 4.65e+05 2.55e+08 1.74e-02 0s
41 6.14734580e-01 6.12315164e-01 5.12e+05 3.95e+08 9.86e-02 0s
42 6.16108808e-01 5.91858039e-01 3.94e+05 3.83e+09 1.33e+00 0s
43 5.51667285e-01 5.78813309e-01 6.30e+05 4.60e+09 1.91e+00 0s
44 6.59529288e-01 5.81310583e-01 5.30e+05 5.47e+09 3.54e+00 0s
45 6.49683270e-01 4.99397707e-01 3.57e+05 2.24e+10 9.32e+00 0s
46 1.04657199e+00 5.14489538e-01 1.79e+06 2.31e+10 1.64e+01 0s
47 1.22874784e+00 5.01640577e-01 2.64e+06 1.38e+10 3.94e+01 0s
48 9.69607430e-01 4.21418471e-01 2.78e+06 1.42e+10 4.17e+01 0s
49 9.68320353e-01 2.57016980e-01 2.79e+06 1.68e+10 4.94e+01 0s
50 7.07204551e-01 2.75881202e-01 1.47e+06 7.19e+09 1.30e+01 0s
51 6.88526451e-01 -1.40550752e-01 1.61e+06 1.65e+10 3.08e+01 0s
52 7.67940047e-01 -2.28118046e-01 6.45e+06 2.46e+10 4.56e+01 0s

Barrier performed 52 iterations in 0.01 seconds
Sub-optimal termination - objective 6.01396622e-01

In this problem, I have set BarHomogeneous=1, because in a previous attempt, I ended up getting an error message saying that the model is unbounded or infeasible, which is impossible for this problem as far as I understand. Hence, I decided to set the above parameter after reading the article on "Numerical Issues in Gurobi". Furthrermoe, I understood that the barrier method is the only possible choice for QCP problems.

However, still I am in doubt whether the sub-optimal termination is correct, because I see a significant oscillation in the primal and dual residuals for close values of the primal objective ?

Can anyone please share your opinion on this ?

In addition to that, I would really appreciate if anyone could share their ideas for me to improve the accuracy of the sub-optimal termination in this problem.

Thanks in advance.