The performance of MIQP models is not always predictable. Here are the results for a small model we used to reproduce a performance issue with Cplex:
Looks like Cplex is attempting a smart reformulation that fails terribly. An indication is the log line:
Reduced MIQP objective Q matrix has 1 nonzeros.
Also the negative best bound (compare this to the relaxed objective) is an indication.
A small reformulation that simplifies the objective, leads to much better performance:
The same issue is discussed in:
- http://bob4er.blogspot.com/2015/03/quadratic-optimization-mysteries-part-1.html
- http://bob4er.blogspot.com/2015/03/quadratic-optimization-mysteries-part-2.html
With a slight variation of this model we can make Mosek look bad. This variant of the model can be easily linearized, which helps tremendously in this case.
The linearized model solves very easily, although there are some bugs with reporting the correct gap. This gap should be 0%, but instead we see:
Best possible: +inf
Absolute gap: 3.000000E+300
Relative gap: 1.000000