[Coin-discuss] OsiCpx getDualRay

[Matthew Galati]

More info...

For an infeasible LP problem, typically I would expect a dual ray to be 
some row of the basis inverse, y, that satisfies the following:
     yA >= 0 and yb < 0 (i.e., farkas lemma)
or, as I have seen with CLP, it could be the other way,
     yA <= 0 and yb > 0 (i.e., farkas lemma)

But when using CPXdualfarkas I noticed that the ray they produce does 
not necessarily satisfy this.

 From CPX manual, it seems to return a row that satisfies:
   //---
   //--- Assume:
   //---   Ax     >= b
   //---   y^T Ax >= y^T b, y >= 0 (for >=)
   //---
   //--- Let z[j] = u[j], if y^T A[j] > 0
   //---          = l[j], if y^T A[j] < 0
   //---          = arbitrary, otherwise
   //---
   //---   y^T b - y^T A z > 0 ==> contradiction (proof of inf)
   //---
   //---  proof_p = y^T b - y^T A z
   //---

So, what exactly is the OsiCpx's getDualRay implementation returning?

Thanks,
Matt



> What is the model that is setup in the current implementation of 
> OsiCpx's getDualRay? Also, can we just use the built-in CPXdualfarkas?
>
> Thanks,
> Matt
>
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