Originally posted by: Agomez8

Hi,

I am solving large mixed binary second order cone programming instances, involving many rotated cone constraints, using CPLEX 12.7.1. The instances correspond to minimization instances.

When solving the continuous relaxation (i.e., replacing binary constraints by 0<=xi<=1 ), the optimal objective value reported by CPLEX is larger than the optimal value reported by CPLEX when solving the mixed-binary program using branch-and-bound. Clearly this not make any sense. This gap becomes larger as the size of the problem increases (and for small instances the value of the continuous relaxation is lower).  I believe (but I am not sure) that the optimal value of the mixed-integer problem is correct. The question is: why is this happening? Is there any way to avoid it from happening.

I have attached an instance where this happens. The optimal value of the relaxation is 13.83 and the optimal value of the mixed-integer program is 6.56.

Thanks!

What is the solution status you get when optimizing the relaxation? Could it be that this is CPX_STAT_NUM_BEST (indicating that the solution could not be proved optimal)?

Originally posted by: Agomez8

Hi Daniel,

Yes, that is the solution status. Although not ideal, now I know at least that the solution of the integer program is likely to be optimal, and that I should disregard the continuous relax. Do you know if there is a parameter I could play with to try to get optimal solutions for the relaxation?