NAG Library Routine Document

H02BZF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     N – INTEGERInput

On entry: this must be the same parameter N as supplied to H02BBF.

Constraint: $\mathbf{N}>0$.

2:     M – INTEGERInput

On entry: this must be the same parameter M as supplied to H02BBF.

Constraint: $\mathbf{M}\ge 0$.

3:     BL($\mathbf{N}+\mathbf{M}$) – REAL (KIND=nag_wp) arrayOutput

On exit: if H02BBF exits with $\mathbf{IFAIL}=\mathbf{0}$, $\mathbf{7}$ or $\mathbf{9}$, the values in the array BL contain the lower bounds imposed on the integer solution for all the constraints. The first N elements contain the lower bounds on the variables, and the next M elements contain the lower bounds for the general linear constraints (if any).

4:     BU($\mathbf{N}+\mathbf{M}$) – REAL (KIND=nag_wp) arrayOutput

On exit: if H02BBF exits with $\mathbf{IFAIL}=\mathbf{0}$, $\mathbf{7}$ or $\mathbf{9}$, the values in the array BU contain the upper bounds imposed on the integer solution for all the constraints. The first N elements contain the upper bounds on the variables, and the next M elements contain the upper bounds for the general linear constraints (if any).

5:     CLAMDA($\mathbf{N}+\mathbf{M}$) – REAL (KIND=nag_wp) arrayOutput

On exit: if H02BBF exits with $\mathbf{IFAIL}=\mathbf{0}$, $\mathbf{7}$ or $\mathbf{9}$, the values in the array CLAMDA contain the values of the Lagrange-multipliers for each constraint with respect to the current working set. The first N elements contain the multipliers (reduced costs) for the bound constraints on the variables, and the next M elements contain the multipliers (shadow costs) for the general linear constraints (if any).

6:     ISTATE($\mathbf{N}+\mathbf{M}$) – INTEGER arrayOutput

On exit: if H02BBF exits with $\mathbf{IFAIL}=\mathbf{0}$, $\mathbf{7}$ or $\mathbf{9}$, the values in the array ISTATE indicate the status of the constraints in the working set at an integer solution. Otherwise, ISTATE indicates the composition of the working set at the final iterate. The significance of each possible value of $\mathbf{ISTATE}\left(j\right)$ is as follows.

$\mathbf{ISTATE}\left(j\right)$	Meaning
$-2$	The constraint violates its lower bound by more than TOLFES (the feasibility tolerance, see H02BBF).
$-1$	The constraint violates its upper bound by more than TOLFES.
$\phantom{-}0$	The constraint is satisfied to within TOLFES, but is not in the working set.
$\phantom{-}1$	This inequality constraint is included in the working set at its lower bound.
$\phantom{-}2$	This inequality constraint is included in the working set at its upper bound.
$\phantom{-}3$	This constraint is included in the working set as an equality. This value of ISTATE can occur only when $\mathbf{BL}\left(j\right)=\mathbf{BU}\left(j\right)$.
$\phantom{-}4$	This corresponds to an integer solution being declared with $x_j$ being temporarily fixed at its current value. This value of ISTATE can occur only when $\mathbf{IFAIL}=\mathbf{0}$, $\mathbf{7}$ or $\mathbf{9}$ on exit from H02BBF.

7:     IWORK(LIWORK) – INTEGER arrayCommunication Array

On entry: this must be the same parameter IWORK as supplied to H02BBF. It is used to pass information from H02BBF to H02BZF and therefore the contents of this array must not be changed before calling H02BZF.

8:     LIWORK – INTEGERInput

On entry: the dimension of the array IWORK as declared in the (sub)program from which H02BZF is called.

9:     RWORK(LRWORK) – REAL (KIND=nag_wp) arrayCommunication Array

On entry: this must be the same parameter RWORK as supplied to H02BBF. It is used to pass information from H02BBF to H02BZF and therefore the contents of this array must not be changed before calling H02BZF.

10:   LRWORK – INTEGERInput

On entry: the dimension of the array RWORK as declared in the (sub)program from which H02BZF is called.

11:   IFAIL – INTEGERInput/Output

On entry: IFAIL must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction for details.

For environments where it might be inappropriate to halt program execution when an error is detected, the value $-1\text{ or }1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this parameter, the recommended value is $0$. When the value $-\mathbf{1}\text{ or }\mathbf{1}$ is used it is essential to test the value of IFAIL on exit.

On exit: $\mathbf{IFAIL}=\mathbf{0}$ unless the routine detects an error or a warning has been flagged (see Section 6).

6  Error Indicators and Warnings

$\mathbf{IFAIL}=1$

On entry,	$\mathbf{N}\le 0$,
or	$\mathbf{M}<0$.

7  Accuracy

8  Further Comments

9  Example

9.1  Program Text

Program Text (h02bzfe.f90)

9.2  Program Data

Program Data (h02bzfe.d)

9.3  Program Results

Program Results (h02bzfe.r)