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.