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FarkasDual
| Type: | double |
|---|---|
| Modifiable: | No |
Together, attributes FarkasDual and
FarkasProof provide a certificate of
infeasibility for the given infeasible problem.
Specifically, FarkasDual
provides a vector 
that can be used to form the following
inequality from the original constraints that is trivially infeasible
within the bounds of the variables:
This inequality is valid even if the original constraints
have a mix of less-than and greater-than senses
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 gives
the value of 
.
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.
