e04rcf is a part of the NAG optimization modelling suite and sets a given property to a subset of the decision variables, particularly, it specifies if the variables are integral or continuous.

2 Specification

Fortran Interface

Subroutine e04rcf (

handle, ptype, lidx, idx, ifail)

Integer, Intent (In)	::	lidx, idx(lidx)
Integer, Intent (Inout)	::	ifail
Character (*), Intent (In)	::	ptype
Type (c_ptr), Intent (In)	::	handle

C Header Interface

#include <nag.h>

void	e04rcf_ (void *handle, const char ptype, const Integer lidx, const Integer idx[], Integer ifail, const Charlen length_ptype)

The routine may be called by the names e04rcf or nagf_opt_handle_set_property.

3 Description

After the model has been fully or partially built by calling routines of the NAG optimization modelling suite, e04rcf may be used to change properties of a subset of the variables in the model. The property is given by ptype which refers to the integrality of the variables (continuous, integer or binary) or their linearity (if the variables are linear or generic, see Section 3.1). Both classes of properties can be set independently, however, only one property per class of properties can be chosen (i.e., a variable can be linear and integer but it cannot be continuous and binary at the same time). The properties can be changed multiple times and the last setting is the one used. e04ryf may be used to display the properties and further details of the problem.

See Section 3.1 in the E04 Chapter Introduction for more details about the NAG optimization modelling suite.

3.1 Linearity of the Variables

It is sometimes useful in Nonlinear Programming (NLP) problems to distinguish between linear and nonlinear variables and thus give the solvers an extra piece of information to utilize. A variable is said to be linear if its involvement in the whole optimization model is linear, i.e., it appears only in linear expressions. All other variables, if used at all, are nonlinear.

Let's assume that we have a problem with seven variables with two nonlinear constraints declared by e04rkf and defined as follows:

g (x) = (\begin{matrix} 3 x_{1} + e^{x_{2}} x_{4} + 4 x_{4} - x_{3} + x_{5} \\ x_{2} + x_{3}^{2} - 3 x_{5} \end{matrix})

and with a linear objective function, linear constraints. Variables

x_{6}

and

x_{7}

are not used at all in the definition of

g (x)

and, therefore, they are clearly linear which is automatically detected by the solver. Although

x_{1}

and

x_{5}

appear in the nonlinear constraints

g (x)

, they are involved only in linear expressions and, therefore, are also linear. These two cannot be detected by the solver because the solver can only see the sparsity pattern defined by e04rkf and a Black Box call-back. In this case, it might be beneficial to set their property as linear using this routine. If no property is set, it is assumed that the variables are generic, meaning that they have no special property, and their linearity is auto detected based on the constraints they appear in. There are no solvers in the suite which would exploit this property at the current release.

4 References

None.

5 Arguments

1: $handle$ – Type (c_ptr) Input

On entry: the handle to the problem. It needs to be initialized (e.g., by e04raf) and must not be changed between calls to the NAG optimization modelling suite.

2: $ptype$ – Character(*) Input

On entry: indicates the property to set for the specified variables. ptype is case insensitive.

Class of properties referring to integrality:

$ptype ='CONTINUOUS'$ or $'CONT'$: The variables will be continuous (the default property).
$ptype ='INTEGER'$ or $'INT'$: The variables become integer.
$ptype ='BINARY'$ or $'BIN'$: The variables become binary so they will be able to hold only values 0 or 1. Note that any existing box bounds are preserved. For example, if variable $x_{42}$ has its bounds set as $1.0 \leq x_{42} \leq 5.3$ and becomes binary, its box bounds are not removed and, therefore, the only allowed value will be $x_{42} = 1.0$ .

Class of properties referring to linearity.

$ptype ='GENERIC'$ or $'GEN'$: The variables have no special property. If they appear in at least one nonlinear expression (constraints or the objective), they will be assumed to be nonlinear (the default property).
$ptype ='LINEAR'$ or $'LIN'$: The variables will be assumed to be linear in all nonlinear constraints and the objective they might appear.

Constraint:

ptype ='BINARY'

'BIN'

'CONTINUOUS'

'CONT'

'GENERIC'

'GEN'

'INTEGER'

'INT'

'LINEAR'

'LIN'

3: $lidx$ – Integer Input

On entry: the number of variables in the index set.

Constraint:

lidx \geq 1

4: $idx (lidx)$ – Integer array Input

On entry: the index set of variables whose properties will be modified. The elements may be supplied in any order.

Constraint:

1 \leq idx (i) \leq n

, for

i = 1, 2, \dots, lidx

, where

n

is the number of decision variables in the problem.

5: $ifail$ – Integer Input/Output

On entry: ifail must be set to

0

−1

1

to set behaviour on detection of an error; these values have no effect when no error is detected.

A value of

0

causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of

−1

means that an error message is printed while a value of

1

means that it is not.

If halting is not appropriate, the value

−1

1

is recommended. If message printing is undesirable, then the value

1

is recommended. Otherwise, the value

−1

is recommended. When the value $- 1$ or $1$ is used it is essential to test the value of ifail on exit.

On exit:

ifail = 0

unless the routine detects an error or a warning has been flagged (see Section 6).

6 Error Indicators and Warnings

If on entry

ifail = 0

−1

, explanatory error messages are output on the current error message unit (as defined by x04aaf).

Errors or warnings detected by the routine:

$ifail = 1$: The supplied handle does not define a valid handle to the data structure for the NAG optimization modelling suite. It has not been properly initialized or it has been corrupted.

$ifail = 2$: The problem cannot be modified right now, the solver is running.

$ifail = 5$: On entry, $lidx = ⟨ value ⟩$ .
Constraint: $lidx \geq 1$ .

$ifail = 6$: On entry, $ptype = ⟨ value ⟩$ .
Constraint: $ptype ='BIN'$ , $'CONT'$ , $'GEN'$ , $'INT'$ or $'LIN'$ .

$ifail = 8$: On entry, $i = ⟨ value ⟩$ , $idx (i) = ⟨ value ⟩$ and $n = ⟨ value ⟩$ .
Constraint: $1 \leq idx (i) \leq n$ .

$ifail = - 99$: An unexpected error has been triggered by this routine. Please contact NAG.
See Section 7 in the Introduction to the NAG Library FL Interface for further information.

$ifail = - 399$: Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library FL Interface for further information.

$ifail = - 999$: Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL Interface for further information.

7 Accuracy

Not applicable.

8 Parallelism and Performance

e04rcf is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.

Please consult the X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this routine. Please also consult the Users' Note for your implementation for any additional implementation-specific information.