: contains the dual solution vector. The magnitude of
gives a measure of the improvement in the objective value if the corresponding bound were to be relaxed so that
could take different values.
A value of
${\mathbf{W}}\left(i\right)$ equal to the special value
$-999.0$ is indicative of the matrix
$A$ not having full rank. It is only likely to occur when
${\mathbf{ITYPE}}=1$. However a matrix may have less than full rank without
${\mathbf{W}}\left(i\right)$ being set to
$-999.0$. If
${\mathbf{ITYPE}}=1$ then the values contained in
W (other than those set to
$-999.0$) may be unreliable; the corresponding values in
INDX may likewise be unreliable. If you have any doubts set
${\mathbf{ITYPE}}=0$. Otherwise the values of
${\mathbf{W}}\left(i\right)$ have the following meaning:
- ${\mathbf{W}}\left(i\right)=0$
- if ${x}_{i}$ is unconstrained.
- ${\mathbf{W}}\left(i\right)<0$
- if ${x}_{i}$ is constrained by its lower bound.
- ${\mathbf{W}}\left(i\right)>0$
- if ${x}_{i}$ is constrained by its upper bound.
- ${\mathbf{W}}\left(i\right)$
- may be any value if ${l}_{i}={u}_{i}$.