e04 Chapter Contents
e04 Chapter Introduction
NAG Library Manual

# NAG Library Function Documentnag_opt_handle_set_nlnobj (e04rgc)

## 1  Purpose

nag_opt_handle_set_nlnobj (e04rgc) is a part of the NAG optimization modelling suite and declares the objective function of the problem as a nonlinear function with a particular gradient sparsity structure.

## 2  Specification

 #include #include
 void nag_opt_handle_set_nlnobj (void *handle, Integer nnzfd, const Integer idxfd[], NagError *fail)

## 3  Description

After the initialization function nag_opt_handle_init (e04rac) has been called (and unless the objective function has been defined previously by nag_opt_handle_set_linobj (e04rec), nag_opt_handle_set_quadobj (e04rfc) or by nag_opt_handle_set_nlnobj (e04rgc)), nag_opt_handle_set_nlnobj (e04rgc) may be used to declare the objective function of the problem as a nonlinear function and define the sparsity pattern (list of nonzero elements) of its gradient. This objective function will typically be used for nonlinear programming problems (NLP) of the kind:
 $minimize x∈ℝn fx (a) subject to lg≤gx≤ug (b) lB≤Bx≤uB (c) lx≤x≤ux (d)$ (1)
The values of the nonlinear objective function $f\left(x\right)$ and the nonzero values of its gradient $\frac{\partial f}{\partial {x}_{i}}$ (matching the sparsity pattern) evaluated at particular points in the decision variable space will be communicated to the NLP solver by user-supplied functions (e.g., objfun and objgrd). See nag_opt_handle_init (e04rac) for more details.

None.

## 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:    $\mathbf{nnzfd}$IntegerInput
On entry: the number of nonzero elements in the sparse gradient vector of the objective function.
Constraint: ${\mathbf{nnzfd}}\ge 0$.
3:    $\mathbf{idxfd}\left[{\mathbf{nnzfd}}\right]$const IntegerInput
On entry: the one-based indices of the nonzero elements of the sparse gradient vector. The indices must be stored in ascending order. Note that $n$, the number of decision variables in the problem, was set in nvar during the initialization of the handle by nag_opt_handle_init (e04rac).
If ${\mathbf{nnzfd}}=0$, the objective is assumed to be zero and the array idxfd will not be referenced and may be NULL.
Constraints:
• $1\le {\mathbf{idxfd}}\left[\mathit{i}-1\right]\le n$, for $\mathit{i}=1,2,\dots ,{\mathbf{nnzfd}}$;
• ${\mathbf{idxfd}}\left[\mathit{i}-1\right]<{\mathbf{idxfd}}\left[\mathit{i}\right]$, for $\mathit{i}=1,2,\dots ,{\mathbf{nnzfd}}-1$.
4:    $\mathbf{fail}$NagError *Input/Output
The NAG error argument (see Section 2.7 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.
The objective function has already been defined.
On entry, argument $〈\mathit{\text{value}}〉$ had an illegal value.
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, ${\mathbf{nnzfd}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{nnzfd}}\ge 0$.
NE_INTARR
On entry, $i=〈\mathit{\text{value}}〉$, ${\mathbf{idxfd}}\left[i-1\right]=〈\mathit{\text{value}}〉$ and $n=〈\mathit{\text{value}}〉$.
Constraint: $1\le {\mathbf{idxfd}}\left[i-1\right]\le n$.
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_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_NOT_INCREASING
On entry, $i=〈\mathit{\text{value}}〉$, ${\mathbf{idxfd}}\left[i-1\right]=〈\mathit{\text{value}}〉$ and ${\mathbf{idxfd}}\left[i\right]=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{idxfd}}\left[\mathit{i}-1\right]<{\mathbf{idxfd}}\left[i\right]$ (ascending order).
NE_PHASE
The Hessians of nonlinear functions have already been defined, a nonlinear objective cannot be added.
The problem cannot be modified in this phase any more, the solver has already been called.

Not applicable.

## 8  Parallelism and Performance

nag_opt_handle_set_nlnobj (e04rgc) is not threaded in any implementation.