NAG CPP Interface
nagcpp::opt::handle_set_simplebounds (e04rh)

1 Purpose

handle_set_simplebounds is a part of the NAG optimization modelling suite and defines bounds on the variables of the problem.

2 Specification

#include "e04/nagcpp_e04rh.hpp"
#include "e04/nagcpp_class_CommE04RA.hpp"
template <typename COMM, typename BL, typename BU>

void function handle_set_simplebounds(COMM &comm, const BL &bl, const BU &bu, OptionalE04RH opt)
template <typename COMM, typename BL, typename BU>

void function handle_set_simplebounds(COMM &comm, const BL &bl, const BU &bu)

3 Description

After the initialization function handle_​init has been called, handle_set_simplebounds may be used to define the variable bounds lxxux of the problem unless the bounds have already been defined. This will typically be used for problems, such as linear programming (LP)
minimize xn cTx   (a) subject to   lBBxuB,   (b) lxxux ,   (c) (1)
quadratic programming (QP)
minimize xn 12 xTHx + cTx   (a) subject to lBBxuB,   (b) lxxux,   (c) (2)
nonlinear programming (NLP)
minimize xn f(x)   (a) subject to lgg(x)ug,   (b) lBBxuB,   (c) lxxux,   (d) (3)
or linear semidefinite programming (SDP)
minimize xn cTx   (a) subject to   i=1 n xi Aik - A0k 0 ,  k=1,,mA ,   (b) lBBxuB,   (c) lxxux,   (d) (4)
where lx and ux are n-dimensional vectors. Note that upper and lower bounds are specified for all the variables. This form allows full generality in specifying various types of constraint. In particular, the jth variable may be fixed by setting lj=uj. If certain bounds are not present, the associated elements of lx or ux 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.
See Section 3.1 in the E04 Chapter Introduction for more details about the NAG optimization modelling suite.

4 References

Candes E and Recht B (2009) Exact matrix completion via convex optimization Foundations of Computation Mathematics (Volume 9) 717–772

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(nvar) double array Input
On entry: lx, bl and ux, bu define lower and upper bounds on the variables, respectively. To fix the jth variable, 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 (i.e., uj=), set bu(j-1)bigbnd.
Constraints:
  • bl(j-1)bu(j-1), for j=1,2,,nvar;
  • bl(j-1)<bigbnd, for j=1,2,,nvar;
  • bu(j-1)>-bigbnd, for j=1,2,,nvar.
3: bu(nvar) double array Input
On entry: lx, bl and ux, bu define lower and upper bounds on the variables, respectively. To fix the jth variable, 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 (i.e., uj=), set bu(j-1)bigbnd.
Constraints:
  • bl(j-1)bu(j-1), for j=1,2,,nvar;
  • bl(j-1)<bigbnd, for j=1,2,,nvar;
  • bu(j-1)>-bigbnd, for j=1,2,,nvar.
4: opt OptionalE04RH Input/Output
Optional parameter container, derived from Optional.

5.1Additional Quantities

1: nvar
n, the number of decision variables x in the problem.

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=3
Variable bounds have already been defined.
errorid=4
On entry, nvar = value,
expected value=value.
Constraint: nvar must match the value given during initialization of comm::handle.
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

10 Example

Examples of the use of this method may be found in the examples for: handle_​solve_​dfls_​rcomm, handle_​solve_​bounds_​foas, handle_​solve_​lp_​ipm, handle_​set_​group and handle_​solve_​ipopt.