Originally posted by: mmsc

Hi everyone

I am solving the following quadratic problem:

Minimize
 obj: 2 z_0 + z_1 + z_2 + z_3 + [ - 2 x_1 * z_1 - 2 x_2 * z_2 - 2 x_3 * z_3
      ] / 2
Subject To
 c1: z_0 + z_1 >= 100
 c2: z_0 + z_2 >= 60
 c3: z_0 + z_3 >= 50
 c4: 2 x_1 + x_2 + x_3 <= 2
Bounds
 0 <= x_1 <= 1
 0 <= x_2 <= 1
 0 <= x_3 <= 1
End

Since the problem is non-convex, I set the solution target to 3 (global optimum). Then, I executed CPLEX 12.6.0.0 which returns the value 200 with z_0 = 100 and the remaining variables 0.

It is easy to see that the solution returned is not optimal since, e.g., x_1=0, x_2=1, x_3=1, z_0=0, z_1=100, z_2=60 and z_3 =50 is feasible and has objective value equal to 100.

Am I doing something wrong? Is this a bug?
 

Thanks in advance.

Originally posted by: EdKlotz

I ran both CPLEX 12.6.3 (the latest available) and 12.6.0.   In both cases CPLEX returns a solution with in objective 200, but in

neither case does it claim that the solution is an optimal one.   Here's the output I get with interactive CPLEX (either version):

        Nodes                                         Cuts/
   Node  Left     Objective  IInf  Best Integer    Best Bound    ItCnt     Gap

      0     0  -1.00000e+37     0      200.0000                      0     ---

Root node processing (before b&c):
  Real time             =    0.00 sec. (0.03 ticks)
Parallel b&c, 4 threads:
  Real time             =    0.00 sec. (0.00 ticks)
  Sync time (average)   =    0.00 sec.
  Wait time (average)   =    0.00 sec.
                          ------------
Total (root+branch&cut) =    0.00 sec. (0.03 ticks)

Solution pool: 1 solution saved.

MIP - Constructed relaxation is unbounded:  Objective =  2.0000000000e+02
Current MIP best bound is infinite.

How does this compare with your runs?   If you got the same thing, then that explains it.   If CPLEX claimed that solution

was optimal, the some additional investigation is need.   Otherwise, if you can put some finite upper bounds on the z variables

in your model, CPLEX then will find the optimal solution with objective 100 that you mention (at least it did for me when I used

upper bounds of 1000 on the z variables).

So you didn't do anything wrong, but you need to always check the solution status, whether it be manually when using

interactive CPLEX, or in your code when calling CPLEX from one of its numerous APIs.

Originally posted by: mmsc

Thank you very much! I forgot to check the solution status.

Assigning upper bounds is easy and can be done systematically to my instances; this enables CPLEX to return the optimal solution.