I have a question regarding the root relaxation objective value.
The problem I am trying to solve is an integer program(IP). I modeled my problem as integer program (i.e. variable types are GRB.INTEGER) and let the state-of-art solver Gurobi to solve it. I get the following root relaxation information from my log:
Root relaxation: objective 2.501961e+02, 3352 iterations, 0.12 seconds
In my own algorithm, I need to solve the continuous relaxation of (IP) at the first step. Therefore, I made the same model but changed the variable types to GRB.CONTINUOUS and let Gurobi to solve it. However, Gurobi cannot find the optimal solution for my continuous model within 1 hour, and the primal objective value is very far away from what I got at the root relaxation.
Iter Primal Dual Primal Dual Compl Time
0 -7.64857345e+00 -1.07326045e+04 3.64e+01 3.85e+00 8.67e+01 123s
1 8.98710957e+00 -1.21394933e+04 3.16e+01 2.85e+00 7.27e+01 223s
2 6.49839807e+03 -1.26663297e+04 1.66e+01 2.49e+00 4.63e+01 325s
3 2.00139518e+03 -1.33834110e+04 4.73e+00 2.74e-06 9.85e+00 428s
4 1.76154917e+03 -4.69790979e+03 4.28e+00 2.81e-10 4.84e+00 529s
5 1.89292310e+03 -1.11126958e+03 3.28e+00 2.87e-10 2.95e+00 632s
6 2.06202435e+03 2.70380221e+03 2.73e+00 1.82e-10 2.04e+00 733s
7 3.74002630e+03 8.63276088e+03 2.10e+00 1.26e-09 1.82e+00 834s
8 8.35114242e+03 1.70416579e+04 1.32e+00 5.75e-08 1.73e+00 935s
9 1.51000919e+04 2.33133433e+04 7.36e-01 2.87e-08 1.93e+00 1036s
10 3.09794008e+04 2.69140853e+04 3.24e-01 5.43e-07 4.37e+00 1138s
11 4.60406989e+04 3.17637908e+04 5.88e-02 2.11e-07 4.69e+00 1240s
12 3.57492040e+04 3.48549626e+04 2.17e-03 4.97e-07 2.87e-01 1341s
13 3.51233448e+04 3.50944852e+04 3.82e-04 5.86e-07 8.97e-03 1443s
Does anyone understand why this happens? My understanding is that the root relaxation solves the same model as my continuous model (general convex), so they should give me the same objective function value.
Thank you so much.
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