Model is unbounded with best objective

[frankshi]

Hi Professor,

I am studying some robust economic dispatch problem. The original min problem has been transformed to max problem based on dual theory, and an MILP can be obtained with big-M constraints. The simplified codes are attached.

I tried to solve the problem with gurobi solver, and the output information is :Model is unbounded. I have tried to find the reason with the steps in " Debugging unbounded models", and the problem is that one part of the objective function is unbounded: 'obj4' in line 73.  However, when I tried to solve the problem with only obj4 in the objective,  I found that one important constraint (line 97) is not active which may cause the problem. I don't know why. Could you help me with it? Thank you very much.

Best regards,

Frank Shi

[Johan Löfberg]

>> optimize([constraint,recover(depends(constraint)) <= 1e8],-objective_total);

>> value(sigma2_pos(1,1,1))

ans =

  -5.6794e+07

[Johan Löfberg]

and line 97 is active after solve

>> sum(sum(rho_pos+rho_neg))

Linear scalar (real, binary, 48 variables)

Current value: 24

(you cannot look at the solution returned when the solver has failed and claimed unbounded)

[frankshi]

Hi Professor,

Thank you very much for your help. It seems that some variables are unbounded. I will double check the model. Thanks again.

[frankshi]

Hi Professor,

I find that the unbounded variables have zero coefficients in the objective function. So that may be the reason of the unbounded model. Thanks. 

[Johan Löfberg]

having 0 coefficients is not necessarily anything bad. Your problem is that some variables can tend to -infinity to help the objective tend to infinity

max x s.t x+y<=1, bad since y can tend to -infinity

max x s.t x+y<=1,y>= 0, ok as x never can be larger than 1

[frankshi]

Hi Professor,

Thanks for your suggestion. You are right. However, I have given the non-negative constraints for all variables in my problem.

With your help, I have further checked the model, and I finally find the reason. Just in ''obj4'', there may be the following problem: max (-1)*x,  s.t. x<=0, then the total model will be unbounded. I have modified the model and reasonable results can be obtained.