NAG CPP Interface
nagcpp::opt::handle_set_nlnconstr (e04rk)

1 Purpose

handle_set_nlnconstr 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 "e04/nagcpp_e04rk.hpp"
#include "e04/nagcpp_class_CommE04RA.hpp"
template <typename COMM, typename BL, typename BU, typename IROWGD, typename ICOLGD>

void function handle_set_nlnconstr(COMM &comm, const BL &bl, const BU &bu, const IROWGD &irowgd, const ICOLGD &icolgd, OptionalE04RK opt)
template <typename COMM, typename BL, typename BU, typename IROWGD, typename ICOLGD>

void function handle_set_nlnconstr(COMM &comm, const BL &bl, const BU &bu, const IROWGD &irowgd, const ICOLGD &icolgd)

3 Description

After the initialization function handle_​init has been called, handle_set_nlnconstr may be used to define the nonlinear constraints lgg(x)ug 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 f(x)   (a) subject to lgg(x)ug,   (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 g(x), 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 handle_set_nlnconstr.
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 handle_​solve_​ipopt).
See Section 3.1 in the E04 Chapter Introduction for more details about the NAG optimization modelling suite.

4 References

None.

5 Arguments

1: comm CommE04RA Input/Output
Communication structure. An object of either the derived class CommE04RA or its base class NoneCopyableComm can be supplied. It is recommended that the derived class is used. If the base class is supplied it must first be initialized via a call to opt::handle_init (e04ra).
2: bl(ncnln) double array 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 .
Constraints:
  • 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.
3: bu(ncnln) double array 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 .
Constraints:
  • 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.
4: irowgd(nnzgd) types::f77_integer array 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 handle_​solve_​ipopt, for l=1,2,,nnzgd.
Constraints:
  • 1irowgd(l-1)ncnln, for l=1,2,,nnzgd;
  • 1icolgd(l-1)n, for l=1,2,,nnzgd.
5: icolgd(nnzgd) types::f77_integer array 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 handle_​solve_​ipopt, for l=1,2,,nnzgd.
Constraints:
  • 1irowgd(l-1)ncnln, for l=1,2,,nnzgd;
  • 1icolgd(l-1)n, for l=1,2,,nnzgd.
6: opt OptionalE04RK Input/Output
Optional parameter container, derived from Optional.

5.1Additional Quantities

1: ncnln
mg, the number of nonlinear constraints (number of rows of the Jacobian matrix).
2: nnzgd
nnzgd gives the number of nonzeros in the Jacobian matrix.

6 Exceptions and Warnings

Errors or warnings detected by the function:
All errors and warnings have an associated numeric error code field, errorid, stored either as a member of the thrown exception object (see errorid), or as a member of opt.ifail, depending on how errors and warnings are being handled (see Error Handling for more details).
Raises: ErrorException
errorid=1
comm::handle has not been initialized.
errorid=1
comm::handle does not belong to the NAG optimization modelling suite,
has not been initialized properly or is corrupted.
errorid=1
comm::handle has not been initialized properly or is corrupted.
errorid=2
The problem cannot be modified in this phase any more, the solver
has already been called.
errorid=2
The Hessian of the nonlinear objective has already been defined,
nonlinear constraints cannot be added.
errorid=3
A set of nonlinear constraints has already been defined.
errorid=6
On entry, nnzgd = value.
Constraint: nnzgd>0.
errorid=6
On entry, ncnln = value.
Constraint: ncnln0.
errorid=8
On entry, i=value, irowgd[i-1]=value and
ncnln=value.
Constraint: 1irowgd[i-1]ncnln.
errorid=8
On entry, i=value, icolgd[i-1]=value and
n=value.
Constraint: 1icolgd[i-1]n.
errorid=8
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.
errorid=10
On entry, j=value, bl[j-1]=value and
bu[j-1]=value.
Constraint: bl[j-1]bu[j-1].
errorid=10
On entry, j=value, bl[j-1]=value,
bigbnd=value.
Constraint: bl[j-1]<bigbnd.
errorid=10
On entry, j=value, bu[j-1]=value,
bigbnd=value.
Constraint: bu[j-1]>-bigbnd.
errorid=10601
On entry, argument value must be a vector of size value array.
Supplied argument has value dimensions.
errorid=10601
On entry, argument value must be a vector of size value array.
Supplied argument was a vector of size value.
errorid=10601
On entry, argument value must be a vector of size value array.
The size for the supplied array could not be ascertained.
errorid=10602
On entry, the raw data component of value is null.
errorid=10603
On entry, unable to ascertain a value for value.
errorid=10605
On entry, the communication class value has not been initialized correctly.
errorid=-99
An unexpected error has been triggered by this routine.
errorid=-399
Your licence key may have expired or may not have been installed correctly.
errorid=-999
Dynamic memory allocation failed.

7 Accuracy

Not applicable.

8 Parallelism and Performance

Please see the description for the underlying computational routine in this section of the FL Interface documentation.

9 Further Comments

None.

10 Example

Examples of the use of this method may be found in the examples for: handle_​solve_​ipopt.