nagcpp::opt::handle_set_linconstr (e04rj) : NAG Library, Mark 27

2 Specification

#include "e04/nagcpp_e04rj.hpp" #include "e04/nagcpp_class_CommE04RA.hpp"

template <typename COMM, typename BL, typename BU, typename IROWB, typename ICOLB, typename B> void function handle_set_linconstr(COMM &comm, const BL &bl, const BU &bu, const IROWB &irowb, const ICOLB &icolb, const B &b, OptionalE04RJ opt)

3 Description

After the initialization function handle_init has been called, handle_set_linconstr may be used to define the linear constraints

l_{B} \leq B x \leq u_{B}

of the problem unless the linear constraints have already been defined. This will typically be used for problems, such as linear programming (LP)

\begin{array}{l} \underset{x \in ℝ^{n}}{minimize} & c^{T} x & (a) \\ subject to & l_{B} \leq B x \leq u_{B}, & (b) \\ l_{x} \leq x \leq u_{x}, & (c) \end{array}

(1)

quadratic programming (QP)

\begin{array}{l} \underset{x \in ℝ^{n}}{minimize} & \frac{1}{2} x^{T} H x + c^{T} x & (a) \\ subject to & l_{B} \leq B x \leq u_{B}, & (b) \\ l_{x} \leq x \leq u_{x}, & (c) \end{array}

(2)

nonlinear programming (NLP)

\begin{array}{l} \underset{x \in ℝ^{n}}{minimize} & f (x) & (a) \\ subject to & l_{g} \leq g (x) \leq u_{g}, & (b) \\ l_{B} \leq B x \leq u_{B}, & (c) \\ l_{x} \leq x \leq u_{x}, & (d) \end{array}

(3)

or linear semidefinite programming (SDP)

\begin{array}{l} \underset{x \in ℝ^{n}}{minimize} & c^{T} x & (a) \\ subject to & \sum_{i = 1}^{n} x_{i} A_{i}^{k} - A_{0}^{k} ⪰ 0, k = 1, \dots, m_{A}, & (b) \\ l_{B} \leq B x \leq u_{B}, & (c) \\ l_{x} \leq x \leq u_{x}, & (d) \end{array}

(4)

where

n

is the number of decision variables,

B

is a general

m_{B} \times n

rectangular matrix and

l_{B}

and

u_{B}

are

m_{B}

-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

j

th constraint may be defined as an equality by setting

l_{j} = u_{j}

. If certain bounds are not present, the associated elements of

l_{B}

u_{B}

may be set to special values that are treated as

- \infty

+ \infty

. 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.

5 Arguments

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).

bl (nclin)

– double array Input

On entry: bl and bu define lower and upper bounds of the linear constraints,

l_{B}

and

u_{B}

, respectively. To define the

j

th constraint as equality, set

bl (j - 1) = bu (j - 1) = β

, where

| β | < bigbnd

. To specify a nonexistent lower bound (i.e.,

l_{j} = - \infty

), set

bl (j - 1) \leq - bigbnd

; to specify a nonexistent upper bound, set

bu (j - 1) \geq bigbnd

Constraints:

$bl (j - 1) \leq bu (j - 1)$ , for $j = 1, 2, \dots, nclin$ ;
$bl (j - 1) < bigbnd$ , for $j = 1, 2, \dots, nclin$ ;
$bu (j - 1) > - bigbnd$ , for $j = 1, 2, \dots, nclin$ ;
if $bl (j - 1) = bu (j - 1)$ , $| bl (j - 1) | < bigbnd$ , for $j = 1, 2, \dots, nclin$ .

bu (nclin)

– double array Input

On entry: bl and bu define lower and upper bounds of the linear constraints,

l_{B}

and

u_{B}

, respectively. To define the

j

th constraint as equality, set

bl (j - 1) = bu (j - 1) = β

, where

| β | < bigbnd

. To specify a nonexistent lower bound (i.e.,

l_{j} = - \infty

), set

bl (j - 1) \leq - bigbnd

; to specify a nonexistent upper bound, set

bu (j - 1) \geq bigbnd

Constraints:

$bl (j - 1) \leq bu (j - 1)$ , for $j = 1, 2, \dots, nclin$ ;
$bl (j - 1) < bigbnd$ , for $j = 1, 2, \dots, nclin$ ;
$bu (j - 1) > - bigbnd$ , for $j = 1, 2, \dots, nclin$ ;
if $bl (j - 1) = bu (j - 1)$ , $| bl (j - 1) | < bigbnd$ , for $j = 1, 2, \dots, nclin$ .

irowb (nnzb)

– types::f77_integer array Input

On entry: arrays irowb, icolb and b store nnzb nonzeros of the sparse matrix

B

in coordinate storage (CS) format (see Section 2.1.1 in the F11 Chapter Introduction). The matrix

B

has dimensions

m_{B} \times n

, where

n

, the number of variables in the problem, was set in nvar during the initialization of the handle by handle_init. irowb specifies one-based row indices, icolb specifies one-based column indices and b specifies the values of the nonzero elements in such a way that

b_{i j} = b (l - 1)

where

i = irowb (l - 1)

and

j = icolb (l - 1)

, for

l = 1, 2, \dots, nnzb

. No particular order of elements is expected, but elements should not repeat.

Constraint:

1 \leq irowb (l - 1) \leq nclin

1 \leq icolb (l - 1) \leq n

, for

l = 1, 2, \dots, nnzb

icolb (nnzb)

– types::f77_integer array Input

On entry: arrays irowb, icolb and b store nnzb nonzeros of the sparse matrix

B

in coordinate storage (CS) format (see Section 2.1.1 in the F11 Chapter Introduction). The matrix

B

has dimensions

m_{B} \times n

, where

n

b_{i j} = b (l - 1)

where

i = irowb (l - 1)

and

j = icolb (l - 1)

, for

l = 1, 2, \dots, nnzb

. No particular order of elements is expected, but elements should not repeat.

Constraint:

1 \leq irowb (l - 1) \leq nclin

1 \leq icolb (l - 1) \leq n

, for

l = 1, 2, \dots, nnzb

b (nnzb)

– double array Input

On entry: arrays irowb, icolb and b store nnzb nonzeros of the sparse matrix

B

in coordinate storage (CS) format (see Section 2.1.1 in the F11 Chapter Introduction). The matrix

B

has dimensions

m_{B} \times n

, where

n

b_{i j} = b (l - 1)

where

i = irowb (l - 1)

and

j = icolb (l - 1)

, for

l = 1, 2, \dots, nnzb

. No particular order of elements is expected, but elements should not repeat.

Constraint:

1 \leq irowb (l - 1) \leq nclin

1 \leq icolb (l - 1) \leq n

, for

l = 1, 2, \dots, nnzb

opt

– OptionalE04RJ Input/Output

Optional parameter container, derived from Optional.

Container for:

idlc – types::f77_integer: This optional parameter may be set using the method OptionalE04RJ::idlc and accessed via OptionalE04RJ::get_idlc.
Default: $0$

Note: idlc is reserved for future releases of the NAG Library.

On entry: if $idlc = 0$ , new linear constraints are added to the problem definition. This is the only value allowed at the moment.

Constraint: $idlc = 0$ .

On exit: the number of the last linear constraint added, thus nclin.

5.1Additional Quantities

1: $nclin$: $m_{B}$ , the number of linear constraints (number of rows of the matrix $B$ ).
2: $nnzb$: nnzb gives the number of nonzeros in matrix $B$

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.

$errorid = 3$: A set of linear constraints has already been defined.

$errorid = 4$: On entry, $idlc = ⟨ value ⟩$ .
Constraint: $idlc = 0$ .

$errorid = 6$: On entry, $nnzb = ⟨ value ⟩$ .
Constraint: $nnzb > 0$ .

$errorid = 6$: On entry, $nclin = ⟨ value ⟩$ .
Constraint: $nclin \geq 0$ .

$errorid = 8$: On entry, $i = ⟨ value ⟩$ , $irowb [i - 1] = ⟨ value ⟩$ and
$nclin = ⟨ value ⟩$ .
Constraint: $1 \leq irowb [i - 1] \leq nclin$ .

$errorid = 8$: On entry, $i = ⟨ value ⟩$ , $icolb [i - 1] = ⟨ value ⟩$ and
$n = ⟨ value ⟩$ .
Constraint: $1 \leq icolb [i - 1] \leq n$ .

$errorid = 8$: On entry, more than one element of b has row index $⟨ value ⟩$
and column index $⟨ value ⟩$ .
Constraint: each element of b must have a unique row and column index.

$errorid = 10$: On entry, $j = ⟨ value ⟩$ , $bl [j - 1] = ⟨ value ⟩$ and
$bu [j - 1] = ⟨ value ⟩$ .
Constraint: $bl [j - 1] \leq bu [j - 1]$ .

$errorid = 10$: 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.

NAG CPP Interface
nagcpp::opt::handle_set_linconstr (e04rj)

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

5.1Additional Quantities

6 Exceptions and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

NAG CPP Interfacenagcpp::opt::handle_set_linconstr (e04rj)

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

5.1Additional Quantities

6 Exceptions and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

NAG CPP Interface
nagcpp::opt::handle_set_linconstr (e04rj)