Originally posted by: ziczyq

Hi All, 

I am using barrier method (CPXbaropt in Callable Library) to solve a large scale QCP problem. Since the .lp file is too large to upload, I shared it through Google Drive. (https://drive.google.com/file/d/1y-PBm51dK4gCj6mLBUQltsDiFDBkOit1/view?usp=sharing)

The link is a minimize MIP problem. First, I solve this MIP problem (CPXmipopt) and obtain the optimal value, say Vmip. Then I solve the relaxation problem, whose variables are all continuous, and obtain the optimal value say Vrp. Theoretically, Vmip should be greater than Vrp (Vmip>Vrp) since Vrp is the optimal value of the corresponding relaxation problem. However, the optimal value from CPLEX is wired. It reports that Vmip<Vrp, which should not happen at all. Could anyone explain why this happens? Thanks!  

I reproduced this issue here with CPLEX 12.8 (Vrp is and Vmip is <= ).

But I am wondering whether this may just be a numerical issue. Your problem statistics do not look good:

Problem name         : example.lp
Objective sense      : Minimize
Variables            : 1830010  [Nneg: 1830000,  General Integer: 10]
Objective nonzeros   : 1530010
Linear constraints   : 2500005  [Less: 1450005,  Greater: 1050000]
  Nonzeros           : 17465962
  RHS nonzeros       : 2499496
Quadratic constraints:   30000  [Less: 30000]
  Linear terms       :       0
  Quadratic terms    :  330000
  RHS nonzeros       :       0

Variables            : Min LB: 0.000000         Max UB: all infinite   
Objective nonzeros   : Min   : 4.768372e-11     Max   : 9.260095       
Linear constraints   :
  Nonzeros           : Min   : 6.675720e-06     Max   : 100.0000       
  RHS nonzeros       : Min   : 6.914139e-06     Max   : 100.0000       
Quadratic constraints:
  Linear terms       : Min   : all zero         Max   : all zero       
  Quadratic terms    : Min   : 1.000000         Max   : 1.000000       
  RHS nonzeros       : Min   : all zero         Max   : all zero

Is there any chance you can shrink the range of numbers? Objective non-zeros range through 12 orders of magnitude!

Originally posted by: ziczyq

Thank you! But I cannot change the formulation of the problem. Do you have the optimal solution for Vrp and Vmip? And is Vrp<Vmip?

Like I said, I could reproduce your problem and indeed have Vrp > Vmip. But given your numbers I am not sure how meaningful those results are.