Dual infeasible due to empty column and unbounded objection

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Menglei Ji

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Apr 16, 2020, 11:32:46 PM4/16/20
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Hi
 
I hope you are doing great!

I am trying to use Benders approach to solve my problem. when I run the code, it shows the error message belows. I have found that my unbounded objective obj2 lead to unbounded results. But I don't know how to correct it. Could you help me?

Attached is my code.

Dual infeasible due to empty column 'x1'.
Presolve time = 0.00 sec. (0.01 ticks)
CPXPARAM_Simplex_Display                         2
CPXPARAM_Barrier_Display                         2
Tried aggregator 1 time.
LP Presolve eliminated 81 rows and 54 columns.
All rows and columns eliminated.
Presolve time = 0.00 sec. (0.02 ticks)

Menglei Ji

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Apr 16, 2020, 11:37:23 PM4/16/20
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bender_paper1.m

Johan Löfberg

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Apr 17, 2020, 12:45:02 AM4/17/20
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It is unbounded as you can, for example, let some elements of e tend to -inf, causing the objective to be arbitrarily small

optimize([C2,obj2 >= -1e6],obj2)
>> value(e)

ans(:,:,1,1,1) =

    -1000420    -1000420
           0          -1
           0           0


ans(:,:,1,1,2) =

     0     0
     0    -1
     0     0


ans(:,:,1,1,3) =

     0     0
     0    -1
     0     0

Menglei Ji

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Apr 17, 2020, 11:27:41 AM4/17/20
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If the subproblem is unbounded, I will add the feasibility cuts with the extreme rays. Now I don't found the function about rays, so, how should i code to get the extreme rays?

Johan Löfberg

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Apr 17, 2020, 11:32:47 AM4/17/20
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there is no support for that via yalmip

Menglei Ji

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Apr 25, 2020, 9:23:09 AM4/25/20
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Professor, when the value of variables is very small，does yalmip show the value is 0, instead of -1e16?

Johan Löfberg

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Apr 25, 2020, 9:26:31 AM4/25/20
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No

>> sdpvar x
>> assign(x,1e-16)
>> x
Linear scalar (real, 1 variable)
Current value: 1e-16
Coefficients range: 1 to 1
>> value(x)

ans =

   1.0000e-16



Menglei Ji

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Apr 25, 2020, 10:33:55 PM4/25/20
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Thanks for your timly response again.  Now my spsol problem has unbounded objective, but the variables and objective have certain values. According to the variable value, my problem should be bounded. Are those values right? and what's the meaning?



value(obj2)

ans =

   540


bender_paper1.m

Johan Löfberg

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Apr 26, 2020, 2:35:00 AM4/26/20
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It's no different from before, the problem is clearly stated as unbounded, and if you don't trust the solver diagnostics

spsol=optimize([C2,obj2>=-1e6],obj2,optionsCeplx)

    yalmipversion: '20200116'
       yalmiptime: 0.2016
       solvertime: 0.0184
             info: 'Successfully solved (CPLEX-IBM)'
          problem: 0


>> value(obj2)

ans =

    -1000000

>> value(e(1,1,1))

ans =

    -1000499



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