Warning: max constraint violation (2.0342e-05) exceeds tolerance

[yongjie wang]

Dear Johan

        Here, the model is a MISOCP problem, and i use gurobi to solve it. However it notes:

Optimize a model with 2856 rows, 2160 columns and 6777 nonzeros

Model has 96 quadratic constraints

Presolve removed 2193 rows and 1149 columns

Presolve time: 0.08s

Presolved: 1047 rows, 1395 columns, 3081 nonzeros

Variable types: 1383 continuous, 12 integer (12 binary)

Root relaxation: objective -1.037639e+06, 417 iterations, 0.00 seconds

    Nodes    |    Current Node    |     Objective Bounds      |     Work

 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

H    0     0                      -0.0465017          -     -      -    0s

*    0     0               0      -0.0642966   -0.06430  0.00%     -    0s

Cutting planes:

Explored 0 nodes (1716 simplex iterations) in 0.28 seconds

Thread count was 4 (of 4 available processors)

Optimal solution found (tolerance 1.00e-04)

Warning: max constraint violation (2.0342e-05) exceeds tolerance

Best objective -6.429657888878e-02, best bound -6.429657888878e-02, gap 0.0%

mubiao =

    0.0643

In my obj, one part is ' detaQch*tumq', and detaQch is zero row vector,and vector 'tumq' constraint is as follow:

con=con+[-M*(1-ZQch)<=tumq-gg<=M*(1-ZQch)];

con=con+[-M*ZQch<=tumq<=M*ZQch];

ZQch are binary,and ,M is big-M,and i make it 100000.

So,it seems that the 'ZQch' can be arbitrary because 'detaQch' is zero. If i make 'ZQch' variable, the result is not right. When i give 'ZQch' one arbitrary value(SOCP NO MI), it is right.

Next,in my model,'detaQch' may not be zero, so the  'ZQch' must be variable,and the warnings appears again.

Many thanks

[yongjie wang]

The value of M is also an important factor, and the obj opt value is different,but the warnings still exists.

[Johan Löfberg]

The problem is ill-defined numericall.

M = 100000 is a recipe for numerical problems. For instance, if the binary variable is 2e-5 (which was the value used in the warning about exceeding tolerance), the constraint -M*ZQch<=tumq<=M*ZQch is -20 <= tumq <= 20, i.e, tumq is very far from being forced to be zero, despite ZQch being essentially 0