NAG Library Function Document

nag_opt_handle_set_nlnhess (e04rlc)

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:    $\mathbf{idf}$ – IntegerInput

On entry: specifies the quantities for which a sparsity structure is provided in nnzh, irowh and icolh.

$\mathbf{idf}=-1$

The sparsity structure of the Hessian of the Lagrangian is provided.

$\mathbf{idf}=0$

The sparsity structure of the Hessian of the objective function is provided.

$\mathbf{idf}>0$

The sparsity structure of the Hessian of the idfth constraint function is provided.

The value of idf will also determine how an NLP solver will call the user-supplied functions that evaluate these nonzeros at particular points of the decision variable space, i.e., whether the solver will expect the nonzero values of the objective and constraint Hessians in separate calls or merged in the Lagrangian Hessian, in one call. See, for example, hess of nag_opt_handle_solve_ipopt (e04stc).

Constraint: $-1\le \mathbf{idf}\le \mathit{ncnln}$.

Note: $\mathit{ncnln}$, the number of nonlinear constraints registered with the handle.

3:    $\mathbf{nnzh}$ – IntegerInput

On entry: the number of nonzero elements in the upper triangle of the matrix $H$.

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

4:    $\mathbf{irowh}\left[\mathbf{nnzh}\right]$ – const IntegerInput

5:    $\mathbf{icolh}\left[\mathbf{nnzh}\right]$ – const IntegerInput

On entry: arrays irowh and icolh store the nonzeros of the upper triangle of the matrix $H$ in coordinate storage (CS) format (see Section 2.1.1 in the f11 Chapter Introduction). irowh specifies one-based row indices, icolh specifies one-based column indices and specifies the values of the nonzero elements in such a way that $h_{ij}=\mathit{H}\left[l-1\right]$ where $i=\mathbf{irowh}\left[l-1\right]$ and $j=\mathbf{icolh}\left[\mathit{l}-1\right]$, for $\mathit{l}=1,2,\dots ,\mathbf{nnzh}$. No particular order is expected, but elements should not repeat.

Constraint: $1\le \mathbf{irowh}\left[\mathit{l}-1\right]\le \mathbf{icolh}\left[\mathit{l}-1\right]\le n$, for $\mathit{l}=1,2,\dots ,\mathbf{nnzh}$.

6:    $\mathbf{fail}$ – 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.

NE_ALREADY_DEFINED

On entry, $\mathbf{idf}=〈\mathit{\text{value}}〉$.
The structure of the Hessian of nonlinear function linked to the given idf has already been defined.

The structure of the Hessian of the Lagrangian has already been defined.

The structure of the individual Hessians has already been defined, the Hessian of the Lagrangian cannot be defined.

NE_BAD_PARAM

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

NE_INT_2

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

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.

An unexpected error has been triggered by this function. Please contact NAG.
See Section 2.7.6 in How to Use the NAG Library and its Documentation for further information.

NE_INVALID_CS

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

On entry, $i=〈\mathit{\text{value}}〉$, $\mathbf{irowh}\left[\mathit{i}-1\right]=〈\mathit{\text{value}}〉$ and $\mathbf{icolh}\left[\mathit{i}-1\right]=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{irowh}\left[\mathit{i}-1\right]\le \mathbf{icolh}\left[\mathit{i}-1\right]$ (elements within the upper triangle).

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

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

Neither nonlinear objective nor nonlinear constraints are present. The structure of the Hessian cannot be defined.

No nonlinear objective has been defined, its Hessian cannot be set.

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

7  Accuracy

8  Parallelism and Performance

9  Further Comments

9.1  Additional Licensor

10  Example