E04RKF is a part of the NAG optimization modelling suite and defines the number of nonlinear constraints of the problem as well as the sparsity structure of their first derivatives.
After the initialization routine
E04RAF has been called, E04RKF may be used to define the nonlinear constraints
${l}_{g}\le g\left(x\right)\le {u}_{g}$ of the problem unless the nonlinear constraints have already been defined. This will typically be used for nonlinear programming problems (NLP) of the kind:
where
$n$ is the number of the decision variables
$x$,
${m}_{g}$ is the number of the nonlinear constraints (in
(1)(b)) and
$g\left(x\right)$,
${l}_{g}$ and
${u}_{g}$ are
${m}_{g}$-dimensional vectors. Linear constraints (
(1)(c)), which require no separate gradient information, can be introduced by
E04RJF and Box constraints (
(1)(d)) can be introduced by
E04RHF.
Note that upper and lower bounds are specified for all the constraints. This form allows full generality in specifying various types of constraint. In particular, the
$j$th constraint may be defined as an equality by setting
${l}_{j}={u}_{j}$. If certain bounds are not present, the associated elements
${l}_{j}$ or
${u}_{j}$ may be set to special values that are treated as
$-\infty $ or
$+\infty $. See the description of the optional parameter
Infinite Bound Size of the solver
E04STF. Its value is denoted as
$\mathit{bigbnd}$ further in this text. Note that the bounds are interpreted based on its value at the time of calling this routine and any later alterations to
Infinite Bound Size will not affect these constraints.
Since each nonlinear constraint is most likely to involve a small subset of the decision variables, the partial derivatives of the constraint functions with respect to those variables are best expressed as a sparse Jacobian matrix of ${m}_{g}$ rows and $n$ columns. The row and column positions of all the nonzero derivatives must be registered with the handle through E04RKF.
The values of the nonlinear constraint functions and their nonzero gradients at particular points in the decision variable space will be communicated to the NLP solver by user-supplied functions (e.g.,
CONFUN and
CONGRD for
E04STF).
None.
If on entry
${\mathbf{IFAIL}}=0$ or
$-1$, explanatory error messages are output on the current error message unit (as defined by
X04AAF).
Not applicable.
E04RKF is not threaded in any implementation.
Parts of the code for
E04STF are distributed according to terms imposed by another licensor. Please refer to
Library Licensors for further details.