NAG CL Interface
e04rkc (handle_​set_​nlnconstr)

1 Purpose

e04rkc 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.

2 Specification

#include <nag.h>
void  e04rkc (void *handle, Integer ncnln, const double bl[], const double bu[], Integer nnzgd, const Integer irowgd[], const Integer icolgd[], NagError *fail)
The function may be called by the names: e04rkc or nag_opt_handle_set_nlnconstr.

3 Description

After the initialization function e04rac has been called, e04rkc may be used to define the nonlinear constraints lggxug of the problem unless the nonlinear constraints have already been defined. This will typically be used for nonlinear programming problems (NLP) of the kind:
minimize xn fx   (a) subject to lggxug,   (b) lBBxuB,   (c) lxxux,   (d) (1)
where n is the number of the decision variables x, mg is the number of the nonlinear constraints (in (1)(b)) and gx, lg and ug are mg-dimensional vectors.
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 jth constraint may be defined as an equality by setting lj=uj. If certain bounds are not present, the associated elements lj or uj may be set to special values that are treated as - or +. See the description of the optional parameter Infinite Bound Size which is common among all solvers in the suite. Its value is denoted as bigbnd further in this text. Note that the bounds are interpreted based on its value at the time of calling this function 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 mg rows and n columns. The row and column positions of all the nonzero derivatives must be registered with the handle through e04rkc.
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 e04stc).
See Section 4.1 in the E04 Chapter Introduction for more details about the NAG optimization modelling suite.

4 References


5 Arguments

1: handle void * Input
On entry: the handle to the problem. It needs to be initialized by e04rac and must not be changed before the call to e04rkc.
2: ncnln Integer Input
On entry: mg, the number of nonlinear constraints (number of rows of the Jacobian matrix).
If ncnln=0, no nonlinear constraints will be defined and bl, bu, nnzgd, irowgd and icolgd will not be referenced and may be NULL.
Constraint: ncnln0.
3: bl[ncnln] const double Input
4: bu[ncnln] const double Input
On entry: bl and bu define lower and upper bounds of the nonlinear constraints, lg and ug, respectively. To define the jth constraint as equality, set bl[j-1] = bu[j-1]=β , where β<bigbnd . To specify a nonexistent lower bound (i.e., lj = - ), set bl[j-1] -bigbnd ; to specify a nonexistent upper bound, set bu[j-1] bigbnd .
  • bl[j-1]bu[j-1], for j=1,2,,ncnln;
  • bl[j-1]<bigbnd, for j=1,2,,ncnln;
  • bu[j-1]>-bigbnd, for j=1,2,,ncnln.
5: nnzgd Integer Input
On entry: nnzgd gives the number of nonzeros in the Jacobian matrix.
Constraint: if ncnln>0, nnzgd>0.
6: irowgd[nnzgd] const Integer Input
7: icolgd[nnzgd] const Integer Input
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 ncnln×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 gi xj where i=irowgd[l-1] and j=icolgd[l-1] should be stored in gdx[l-1] in congrd in e04stc, for l=1,2,,nnzgd.
  • 1irowgd[l-1]ncnln, for l=1,2,,nnzgd;
  • 1icolgd[l-1]n, for l=1,2,,nnzgd.
8: fail NagError * Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
A set of nonlinear constraints has already been defined.
On entry, argument value had an illegal value.
On entry, j=value, bl[j-1]=value, bigbnd=value.
Constraint: bl[j-1]<bigbnd.
On entry, j=value, bl[j-1]=value and bu[j-1]=value.
Constraint: bl[j-1]bu[j-1].
On entry, j=value, bu[j-1]=value, bigbnd=value.
Constraint: bu[j-1]>-bigbnd.
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.
On entry, ncnln=value.
Constraint: ncnln0.
On entry, nnzgd=value.
Constraint: nnzgd>0.
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.
On entry, i=value, icolgd[i-1]=value and n=value.
Constraint: 1icolgd[i-1]n.
On entry, i=value, irowgd[i-1]=value and ncnln=value.
Constraint: 1irowgd[i-1]ncnln.
On entry, more than one element of structural Jacobian matrix has row index value and column index value.
Constraint: each element of structural Jacobian matrix must have a unique row and column index.
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.
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.

7 Accuracy

Not applicable.

8 Parallelism and Performance

e04rkc is not threaded in any implementation.

9 Further Comments


10 Example

See Section 10 in e04stc.