NAG Library Function Document

nag_opt_handle_set_nlnconstr (e04rkc)

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Purpose

2

Specification

3

Description

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References

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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:    $\mathbf{ncnln}$ – 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 and may be NULL.

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

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

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

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 $\mathbf{bl}\left[j-1\right]=\mathbf{bu}\left[j-1\right]=\beta$, 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 $\mathit{j}=1,2,\dots ,\mathbf{ncnln}$;
• $\mathbf{bl}\left[\mathit{j}-1\right]<\mathit{bigbnd}$, for $\mathit{j}=1,2,\dots ,\mathbf{ncnln}$;
• $\mathbf{bu}\left[\mathit{j}-1\right]>-\mathit{bigbnd}$, 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:    $\mathbf{irowgd}\left[\mathbf{nnzgd}\right]$ – const IntegerInput

7:    $\mathbf{icolgd}\left[\mathbf{nnzgd}\right]$ – const IntegerInput

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 $i=\mathbf{irowgd}\left[l-1\right]$ and $j=\mathbf{icolgd}\left[\mathit{l}-1\right]$ should be stored in $\mathbf{gdx}\left[\mathit{l}-1\right]$, for $\mathit{l}=1,2,\dots ,\mathbf{nnzgd}$.

Constraints:

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

8:    $\mathbf{fail}$ – 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 nonlinear 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, $\mathbf{ncnln}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{ncnln}\ge 0$.

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

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

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

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.

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 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.

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Accuracy

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Parallelism and Performance

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Further Comments

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Example