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Why does SOCP obtain a suboptimal solution?




  • Zixian He
    First Comment
    First Question
    Set parameter Threads to value 8
    Set parameter TimeLimit to value 3600
    Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (win64)

    CPU model: AMD Ryzen 7 6800H with Radeon Graphics, instruction set [SSE2|AVX|AVX2]
    Thread count: 8 physical cores, 16 logical processors, using up to 8 threads

    Optimize a model with 35952 rows, 26928 columns and 180654 nonzeros
    Model fingerprint: 0x0377dc3d
    Model has 4488 quadratic constraints
    Coefficient statistics:
    Matrix range [1e+00, 5e+03]
    QMatrix range [1e+00, 1e+00]
    Objective range [3e-04, 5e+03]
    Bounds range [1e+00, 1e+00]
    RHS range [1e+00, 5e+04]
    Presolve removed 2154 rows and 1931 columns
    Presolve time: 0.05s
    Presolved: 47262 rows, 33973 columns, 197583 nonzeros
    Presolved model has 4488 second-order cone constraints
    Ordering time: 0.01s

    Barrier statistics:
    AA' NZ : 5.996e+05
    Factor NZ : 1.513e+06 (roughly 45 MB of memory)
    Factor Ops : 6.985e+07 (less than 1 second per iteration)
    Threads : 8

    Objective Residual
    Iter Primal Dual Primal Dual Compl Time
    0 9.17940430e+08 1.16777778e+07 5.48e+03 5.04e+01 3.12e+04 0s
    1 2.74717996e+08 -4.26543783e+06 1.30e+03 3.35e+01 1.12e+04 0s
    2 1.25578432e+08 3.34626544e+06 3.95e+02 1.14e+01 3.99e+03 0s
    3 7.99429462e+07 2.77429203e+07 2.01e+02 4.77e+00 2.06e+03 0s
    4 5.68975154e+07 4.80616364e+07 1.19e+02 2.00e+00 1.06e+03 0s
    5 3.99230356e+07 5.02889772e+07 6.23e+01 1.28e+00 6.25e+02 0s
    6 3.54935926e+07 5.83556484e+07 4.73e+01 8.64e-01 4.37e+02 0s
    7 3.00547679e+07 5.83689346e+07 2.92e+01 5.40e-01 3.35e+02 0s
    8 2.81408345e+07 5.91774707e+07 2.23e+01 4.03e-01 2.70e+02 0s
    9 2.47493214e+07 4.95193859e+07 1.07e+01 1.84e-01 2.03e+02 0s
    10 2.26700632e+07 4.38902281e+07 4.53e+00 1.19e-01 1.99e+02 0s
    11 2.16904326e+07 3.22947106e+07 1.61e+00 5.02e-02 8.99e+01 0s
    12 2.13703771e+07 2.90305587e+07 8.52e-01 3.52e-02 6.32e+01 0s
    13 2.12076746e+07 2.74405731e+07 6.03e-01 2.83e-02 5.21e+01 0s
    14 2.08463586e+07 2.54278217e+07 1.29e-01 2.02e-02 3.85e+01 0s
    15 2.06809444e+07 2.40681413e+07 1.06e-01 1.48e-02 2.92e+01 0s
    16 2.04994950e+07 2.32358058e+07 9.04e-02 1.18e-02 2.48e+01 0s
    17 2.02686417e+07 2.26331546e+07 6.60e-02 9.62e-03 2.06e+01 1s
    18 2.01228268e+07 2.17653763e+07 5.59e-02 6.84e-03 1.66e+01 1s
    19 2.00028593e+07 2.12940771e+07 4.41e-02 5.34e-03 1.36e+01 1s
    20 1.99506895e+07 2.11542383e+07 3.92e-02 4.87e-03 1.24e+01 1s
    21 1.98753077e+07 2.07808612e+07 3.28e-02 3.73e-03 1.02e+01 1s
    22 1.98056691e+07 2.03784291e+07 2.54e-02 2.49e-03 7.51e+00 1s
    23 1.97437146e+07 2.00401475e+07 1.76e-02 1.41e-03 4.67e+00 1s
    24 1.96890094e+07 1.98125705e+07 9.48e-03 6.68e-04 2.34e+00 1s
    25 1.96630034e+07 1.97271076e+07 5.95e-03 3.87e-04 1.43e+00 1s
    26 1.96431837e+07 1.96822867e+07 3.58e-03 2.36e-04 8.54e-01 1s
    27 1.96314026e+07 1.96443047e+07 2.18e-03 1.09e-04 4.50e-01 1s
    28 1.96204054e+07 1.96302870e+07 1.04e-03 6.16e-05 2.14e-01 1s
    29 1.96165061e+07 1.96217870e+07 6.50e-04 3.26e-05 1.08e-01 1s
    30 1.96137516e+07 1.96140515e+07 4.82e-04 6.82e-06 2.03e-02 1s
    31 1.96131230e+07 1.96129102e+07 1.25e-04 1.77e-07 2.76e-03 1s
    32 1.96129314e+07 1.96129167e+07 6.23e-05 2.10e-07 1.80e-04 1s
    33 1.96129056e+07 1.96129169e+07 1.22e+01 1.52e-02 3.02e-05 1s
    34 1.96129086e+07 1.96129169e+07 1.22e+01 1.53e-02 3.01e-05 1s
    35 1.96129104e+07 1.96129170e+07 1.10e+01 2.58e-02 2.57e-05 1s
    36 1.96127358e+07 1.96129170e+07 1.59e+01 8.52e-03 1.29e-05 1s
    37 1.96127286e+07 1.96129170e+07 2.45e+01 1.62e-02 1.14e-05 1s
    38 1.96127888e+07 1.96129170e+07 3.94e+01 3.02e-02 7.97e-06 1s
    39 1.96128136e+07 1.96129170e+07 3.16e+01 5.20e-02 6.57e-06 1s
    40 1.96128892e+07 1.96129171e+07 2.10e+01 1.04e-01 4.97e-06 2s
    41 1.96129837e+07 1.96129171e+07 4.06e+01 2.01e-01 3.81e-06 2s
    42 1.96130379e+07 1.96129171e+07 5.39e+01 2.28e-01 3.40e-06 2s
    43 1.96132273e+07 1.96129171e+07 1.41e+02 3.69e-01 2.39e-06 2s
    44 1.96129770e+07 1.96129171e+07 1.95e+01 2.72e-01 7.09e-07 2s
    45 1.96131802e+07 1.96129171e+07 7.34e+01 5.22e-01 6.61e-07 2s
    46 1.96127051e+07 1.96129171e+07 1.40e+02 1.02e+00 5.75e-07 2s
    47 1.96129541e+07 1.96129172e+07 1.22e+02 2.68e+00 4.65e-07 2s
    48 1.96131479e+07 1.96129172e+07 1.32e+02 2.50e+00 2.48e-07 2s
    49 1.96132796e+07 1.96129172e+07 1.59e+02 2.60e+00 2.24e-07 2s
    50 1.96127509e+07 1.96129172e+07 1.64e+02 3.64e+00 2.03e-07 2s
    51 1.96130932e+07 1.96129172e+07 1.89e+02 4.12e+00 1.93e-07 2s
    52 1.96130342e+07 1.96129172e+07 1.57e+02 4.72e+00 1.82e-07 2s
    53 1.96135314e+07 1.96129172e+07 1.52e+02 4.90e+00 1.75e-07 2s
    54 1.96134952e+07 1.96129172e+07 1.55e+02 4.91e+00 1.74e-07 2s
    55 1.96117425e+07 1.96129172e+07 1.65e+02 5.74e+00 1.61e-07 3s
    56 1.96129761e+07 1.96129172e+07 2.01e+02 8.77e+00 1.18e-07 3s
    57 1.96139275e+07 1.96129172e+07 3.22e+02 1.37e+01 7.78e-08 3s
    58 1.96128024e+07 1.96129172e+07 4.02e+02 2.09e+01 6.61e-08 3s
    59 1.96133383e+07 1.96129172e+07 4.87e+02 2.24e+01 6.34e-08 3s
    60 1.96140276e+07 1.96129172e+07 6.78e+02 3.52e+01 5.21e-08 3s
    61 1.96118055e+07 1.96129172e+07 1.05e+03 4.25e+01 4.02e-08 3s
    62 1.96097664e+07 1.96129172e+07 1.85e+03 5.77e+01 3.80e-08 3s
    63 1.96083524e+07 1.96129172e+07 2.19e+03 8.27e+01 3.44e-08 3s
    64 1.95888606e+07 1.96129172e+07 3.23e+03 9.01e+01 3.28e-08 3s
    65 1.96298356e+07 1.96129172e+07 4.36e+03 8.97e+01 3.23e-08 3s
    66 1.96767296e+07 1.96129172e+07 6.61e+03 9.21e+01 3.15e-08 3s
    67 1.96609988e+07 1.96129172e+07 9.98e+03 9.33e+01 2.99e-08 4s
    68 1.96609988e+07 1.96129172e+07 9.98e+03 9.33e+01 2.99e-08 4s
    69 1.96439202e+07 1.96129172e+07 1.09e+04 1.02e+02 2.95e-08 4s
    70 1.95423986e+07 1.96129172e+07 2.22e+04 1.61e+02 2.82e-08 4s
    71 1.95358451e+07 1.96129172e+07 2.26e+04 1.63e+02 2.76e-08 4s
    72 1.92815283e+07 1.96129172e+07 3.97e+04 1.63e+02 2.83e-08 4s
    73 1.89616188e+07 1.96129172e+07 5.18e+04 3.70e+02 7.74e-08 4s

    Barrier performed 73 iterations in 4.07 seconds (4.72 work units)
    Sub-optimal termination - objective 1.96129314e+07
  • Jaromił Najman
    Gurobi Staff Gurobi Staff

    Sub-optimal termination is printed when the barrier algorithm does not make any (or only very small) progress in the solution value and cannot decrease the dual residual, meaning that although the final convergence criterion is met, the dual infeasibility cannot be reduced. It then terminates at some point and returns the last most feasible iterate, which is declared as sub-optimal. This is often the case for numerically questionable models. 

    You can try to overcome this issue by either reformulating your problem and/or experimenting with the following parameters; this may however result in a performance loss:

    You should also try upgrading to Gurobi v11.

    Best regards, 


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