NAG Library Routine Document

e04rkf  (handle_set_nlnconstr)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:     $\mathbf{handle}$ – Type (c_ptr)Input

On entry: the handle to the problem. It needs to be initialized by e04raf and must not be changed.

2:     $\mathbf{ncnln}$ – IntegerInput

On entry: $m_g$, the number of nonlinear constraints (number of rows of the Jacobian matrix).

If $\mathbf{ncnln}=0$, no nonlinear constraints will be defined and bl, bu, nnzgd, irowgd and icolgd will not be referenced.

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

3:     $\mathbf{bl}\left(\mathbf{ncnln}\right)$ – Real (Kind=nag_wp) arrayInput

4:     $\mathbf{bu}\left(\mathbf{ncnln}\right)$ – Real (Kind=nag_wp) arrayInput

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

Constraints:

• $\mathbf{bl}\left(\mathit{j}\right)\le \mathbf{bu}\left(\mathit{j}\right)$, for $\mathit{j}=1,2,\dots ,\mathbf{ncnln}$;
• $\mathbf{bl}\left(\mathit{j}\right)<\mathit{bigbnd}$, for $\mathit{j}=1,2,\dots ,\mathbf{ncnln}$;
• $\mathbf{bu}\left(\mathit{j}\right)>-\mathit{bigbnd}$, for $\mathit{j}=1,2,\dots ,\mathbf{ncnln}$.

5:     $\mathbf{nnzgd}$ – IntegerInput

On entry: nnzgd gives the number of nonzeros in the Jacobian matrix.

Constraint: if $\mathbf{ncnln}>0$, $\mathbf{nnzgd}>0$.

6:     $\mathbf{irowgd}\left(\mathbf{nnzgd}\right)$ – Integer arrayInput

7:     $\mathbf{icolgd}\left(\mathbf{nnzgd}\right)$ – Integer arrayInput

On entry: arrays irowgd and icolgd store the sparsity structure (pattern) of the Jacobian matrix as nnzgd nonzeros in coordinate storage (CS) format (see Section 2.1.1 in the F11 Chapter Introduction). The matrix has dimensions $\mathbf{ncnln}\times n$. irowgd specifies one-based row indices and icolgd specifies one-based column indices. No particular order of elements is expected, but elements should not repeat and the same order should be used when the Jacobian is evaluated for the solver, e.g., the value of $\frac{\partial g_i}{\partial x_j}$ where $i=\mathbf{irowgd}\left(l\right)$ and $j=\mathbf{icolgd}\left(\mathit{l}\right)$ should be stored in $\mathbf{gdx}\left(\mathit{l}\right)$, for $\mathit{l}=1,2,\dots ,\mathbf{nnzgd}$.

Constraints:

• $1\le \mathbf{irowgd}\left(\mathit{l}\right)\le \mathbf{ncnln}$, for $\mathit{l}=1,2,\dots ,\mathbf{nnzgd}$;
• $1\le \mathbf{icolgd}\left(\mathit{l}\right)\le n$, for $\mathit{l}=1,2,\dots ,\mathbf{nnzgd}$.

8:     $\mathbf{ifail}$ – IntegerInput/Output

On entry: ifail must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this argument you should refer to Section 3.4 in How to Use the NAG Library and its Documentation 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, the recommended value is $-1$. When the value $-\mathbf{1}\text{ or }1$ 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

$\mathbf{ifail}=1$

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 e04raf or it has been corrupted.

$\mathbf{ifail}=2$

The Hessian of the nonlinear objective has already been defined, nonlinear constraints cannot be added.

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

$\mathbf{ifail}=3$

A set of nonlinear constraints has already been defined.

$\mathbf{ifail}=6$

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

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

$\mathbf{ifail}=8$

On entry, $i=〈\mathit{\text{value}}〉$, $\mathbf{icolgd}\left(\mathit{i}\right)=〈\mathit{\text{value}}〉$ and $n=〈\mathit{\text{value}}〉$.
Constraint: $1\le \mathbf{icolgd}\left(\mathit{i}\right)\le n$.

On entry, $i=〈\mathit{\text{value}}〉$, $\mathbf{irowgd}\left(\mathit{i}\right)=〈\mathit{\text{value}}〉$ and $\mathbf{ncnln}=〈\mathit{\text{value}}〉$.
Constraint: $1\le \mathbf{irowgd}\left(\mathit{i}\right)\le \mathbf{ncnln}$.

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

$\mathbf{ifail}=10$

On entry, $j=〈\mathit{\text{value}}〉$, $\mathbf{bl}\left(j\right)=〈\mathit{\text{value}}〉$, $\mathit{bigbnd}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{bl}\left(j\right)<\mathit{bigbnd}$.

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

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

$\mathbf{ifail}=-99$

An unexpected error has been triggered by this routine. Please contact NAG.

See Section 3.9 in How to Use the NAG Library and its Documentation for further information.

$\mathbf{ifail}=-399$

Your licence key may have expired or may not have been installed correctly.

See Section 3.8 in How to Use the NAG Library and its Documentation for further information.

$\mathbf{ifail}=-999$

Dynamic memory allocation failed.

See Section 3.7 in How to Use the NAG Library and its Documentation for further information.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example