NAG Library Function Document

nag_opt_handle_set_linconstr (e04rjc)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:    $\mathbf{handle}$ – void *Input

On entry: the handle to the problem. It needs to be initialized by nag_opt_handle_init (e04rac) and must not be changed.

2:    $\mathbf{nclin}$ – IntegerInput

On entry: $m_B$, the number of linear constraints (number of rows of the matrix $B$).

If $\mathbf{nclin}=0$, no linear constraints will be defined and bl, bu, nnzb, irowb, icolb and b will not be referenced and may be NULL.

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

3:    $\mathbf{bl}\left[\mathbf{nclin}\right]$ – const doubleInput

4:    $\mathbf{bu}\left[\mathbf{nclin}\right]$ – const doubleInput

On entry: bl and bu define lower and upper bounds of the linear constraints, $l_B$ and $u_B$, respectively. To define the $j$th constraint as equality, set $\mathbf{bl}\left[j-1\right]=\mathbf{bu}\left[j-1\right]=\beta$, where $\left|\beta \right|<\mathit{bigbnd}$. To specify a nonexistent lower bound (i.e., $l_j=-\infty$), set $\mathbf{bl}\left[j-1\right]\le -\mathit{bigbnd}$; to specify a nonexistent upper bound, set $\mathbf{bu}\left[j-1\right]\ge \mathit{bigbnd}$.

Constraints:

• $\mathbf{bl}\left[\mathit{j}-1\right]\le \mathbf{bu}\left[\mathit{j}-1\right]$, for $\mathit{j}=1,2,\dots ,\mathbf{nclin}$;
• $\mathbf{bl}\left[\mathit{j}-1\right]<\mathit{bigbnd}$, for $\mathit{j}=1,2,\dots ,\mathbf{nclin}$;
• $\mathbf{bu}\left[\mathit{j}-1\right]>-\mathit{bigbnd}$, for $\mathit{j}=1,2,\dots ,\mathbf{nclin}$;
• if $\mathbf{bl}\left[\mathit{j}-1\right]=\mathbf{bu}\left[\mathit{j}-1\right]$, $\left|\mathbf{bl}\left[\mathit{j}-1\right]\right|<\mathit{bigbnd}$, for $\mathit{j}=1,2,\dots ,\mathbf{nclin}$.

5:    $\mathbf{nnzb}$ – IntegerInput

On entry: nnzb gives the number of nonzeros in matrix $B$.

Constraint: if $\mathbf{nclin}>0$, $\mathbf{nnzb}>0$.

6:    $\mathbf{irowb}\left[\mathbf{nnzb}\right]$ – const IntegerInput

7:    $\mathbf{icolb}\left[\mathbf{nnzb}\right]$ – const IntegerInput

8:    $\mathbf{b}\left[\mathbf{nnzb}\right]$ – const doubleInput

On entry: arrays irowb, icolb and b store nnzb nonzeros of the sparse matrix $B$ in coordinate storage (CS) format (see Section 2.1.1 in the f11 Chapter Introduction). The matrix $B$ has dimensions $m_B\times n$, where $n$, the number of variables in the problem, was set in nvar during the initialization of the handle by nag_opt_handle_init (e04rac). irowb specifies one-based row indices, icolb specifies one-based column indices and b specifies the values of the nonzero elements in such a way that $b_{ij}=\mathbf{b}\left[l-1\right]$ where $i=\mathbf{irowb}\left[l-1\right]$ and $j=\mathbf{icolb}\left[\mathit{l}-1\right]$, for $\mathit{l}=1,2,\dots ,\mathbf{nnzb}$. No particular order of elements is expected, but elements should not repeat.

Constraint: $1\le \mathbf{irowb}\left[\mathit{l}-1\right]\le \mathbf{nclin}$, $1\le \mathbf{icolb}\left[\mathit{l}-1\right]\le n$, for $\mathit{l}=1,2,\dots ,\mathbf{nnzb}$.

9:    $\mathbf{idlc}$ – Integer *Input/Output

Note: idlc is reserved for future releases of the NAG C Library.

On entry: if $\mathbf{idlc}=0$, new linear constraints are added to the problem definition. This is the only value allowed at the moment.

Constraint: $\mathbf{idlc}=0$.

On exit: the number of the last linear constraint added, thus nclin.

10:  $\mathbf{fail}$ – NagError *Input/Output

The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

6

Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.

NE_ALREADY_DEFINED

A set of linear constraints has already been defined.

NE_BAD_PARAM

On entry, argument $〈\mathit{\text{value}}〉$ had an illegal value.

NE_BOUND

On entry, $j=〈\mathit{\text{value}}〉$, $\mathbf{bl}\left[j-1\right]=〈\mathit{\text{value}}〉$, $\mathit{bigbnd}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{bl}\left[j-1\right]<\mathit{bigbnd}$.

On entry, $j=〈\mathit{\text{value}}〉$, $\mathbf{bl}\left[j-1\right]=〈\mathit{\text{value}}〉$ and $\mathbf{bu}\left[j-1\right]=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{bl}\left[j-1\right]\le \mathbf{bu}\left[j-1\right]$.

On entry, $j=〈\mathit{\text{value}}〉$, $\mathbf{bu}\left[j-1\right]=〈\mathit{\text{value}}〉$, $\mathit{bigbnd}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{bu}\left[j-1\right]>-\mathit{bigbnd}$.

NE_HANDLE

The supplied handle does not define a valid handle to the data structure for the NAG optimization modelling suite. It has not been initialized by nag_opt_handle_init (e04rac) or it has been corrupted.

NE_INT

On entry, $\mathbf{nclin}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{nclin}\ge 0$.

On entry, $\mathbf{nnzb}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{nnzb}>0$.

NE_INTERNAL_ERROR

An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 2.7.6 in How to Use the NAG Library and its Documentation for further information.

NE_INVALID_CS

On entry, $i=〈\mathit{\text{value}}〉$, $\mathbf{icolb}\left[\mathit{i}-1\right]=〈\mathit{\text{value}}〉$ and $n=〈\mathit{\text{value}}〉$.
Constraint: $1\le \mathbf{icolb}\left[\mathit{i}-1\right]\le n$.

On entry, $i=〈\mathit{\text{value}}〉$, $\mathbf{irowb}\left[\mathit{i}-1\right]=〈\mathit{\text{value}}〉$ and $\mathbf{nclin}=〈\mathit{\text{value}}〉$.
Constraint: $1\le \mathbf{irowb}\left[\mathit{i}-1\right]\le \mathbf{nclin}$.

On entry, more than one element of b has row index $〈\mathit{\text{value}}〉$ and column index $〈\mathit{\text{value}}〉$.
Constraint: each element of b must have a unique row and column index.

NE_NO_LICENCE

Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.

NE_PHASE

The problem cannot be modified in this phase any more, the solver has already been called.

NE_REF_MATCH

On entry, $\mathbf{idlc}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{idlc}=0$.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (e04rjce.c)

10.2

Program Data

Program Options (e04rjce.opt)

10.3

Program Results

Program Results (e04rjce.r)