I noticed something which I'm not sure whether its intentional.
a) I solve a MIP only for feasibility (obj=0) with MIPGap = 1e-4 and default values for OptimalityTol, IntFeasTol etc...output leads to e.g.:
Optimal solution found (tolerance 1.00e-04)
b) I use the results from a) as warm-start for another optimization of the same MIP but with a non-zero objective this time, output:
User MIP start did not produce a new incumbent solution
User MIP start violates constraint R1161 by 0.000050000
Two questions regarding this:
1. Why could MIPstart violate some constraint by 5e-5 when the tolerances in a) had been of size 1e-6 (FeasibilityTol, OptimalityTol)
2. Would this violation lead to Gurobi not using (all of) the warm-start values?
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