After the initialization function
e04rac has been called and an objective function
or nonlinear constraint function
has been registered with
e04rgc and
e04rkc,
e04rlc can be used to define the sparsity structure of the Hessians,
, of those functions (i.e., the second partial derivatives with respect to the decision variables) or a linear combination of them, called the Lagrangian.
- Defining
;
- the Hessian of the Lagrangian function ;
- the Hessian of the objective function ;
- the Hessian of the constraint functions .
The nonzero values of the Hessians at particular points in the decision variable space will be communicated to the NLP solver by user-supplied functions (e.g.,
hess for
e04stc).
Some NLP solvers (e.g.,
e04stc) expect either all of the Hessians (for objective and nonlinear constraints) to be supplied or none and they will terminate with an error indicator if only some but not all of the Hessians have been introduced by
e04rlc.
Some NLP solvers (e.g.,
e04stc, again) will automatically switch to using internal approximations for the Hessians if none have been introduced by
e04rlc. This usually results in a slower convergence (more iterations to the solution) and might even result in no solution being attainable within the ordinary tolerances.
See
Section 4.1 in the
E04 Chapter Introduction for more details about the NAG optimization modelling suite.
None.
- NE_ALLOC_FAIL
-
Dynamic memory allocation failed.
See
Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
- NE_ALREADY_DEFINED
-
On entry,
.
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 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
e04rac or it has been corrupted.
- NE_INT
-
On entry, .
Constraint: .
- NE_INT_2
-
On entry, .
Constraint: .
- 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 7.5 in the Introduction to the NAG Library CL Interface for further information.
- NE_INVALID_CS
-
On entry, , and .
Constraint: .
On entry, , and .
Constraint: (elements within the upper triangle).
On entry, , and .
Constraint: .
On entry, more than one element of structural matrix has row index and column index .
Constraint: each element of structural 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 8 in the Introduction to the NAG Library CL Interface 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.
Not applicable.
None.