FarkasProof
| Type: | double |
|---|---|
| Modifiable: | No |
Together, attributes FarkasDual and FarkasProof provide a certificate of infeasibility for the given infeasible problem. Specifically, FarkasDual can be used to form the following inequality from the original constraints that is infeasible within the bounds of the variables:
This Farkas constraint is valid, because
if the
-th constraint has a 
sense and
if the
-th constraint has a 
sense.
Let
be the coefficients of this inequality and
be its right hand side. With 
and 
being the lower and upper
bounds of the variables 
we have
if
, and
if 
.
The minimum violation of the Farkas constraint is achieved by setting
for 
and 
for
. Then, we can calculate the minimum violation as
where 
.
The FarkasProof attribute provides
, and the FarkasDual attributes
provide the 
multipliers for the original constraints.
These attributes are only available when parameter InfUnbdInfo is set to 1.
For examples of how to query or modify attributes, refer to our Attribute Examples.
