handle_set_quadobj is a part of the NAG optimization modelling suite and defines or redefines the objective function of the problem to be linear or quadratic.

2 Specification

#include "e04/nagcpp_e04rf.hpp"
#include "e04/nagcpp_class_CommE04RA.hpp"

template <typename COMM, typename IDXC, typename C, typename IROWH, typename ICOLH, typename H>

void function handle_set_quadobj(COMM &comm, const IDXC &idxc, const C &c, const IROWH &irowh, const ICOLH &icolh, const H &h, OptionalE04RF opt)

template <typename COMM, typename IDXC, typename C, typename IROWH, typename ICOLH, typename H>

void function handle_set_quadobj(COMM &comm, const IDXC &idxc, const C &c, const IROWH &irowh, const ICOLH &icolh, const H &h)

3 Description

After the handle has been initialized (e.g., handle_init has been called), handle_set_quadobj may be used to define the objective function of the problem as a quadratic function

c^{T} x + \frac{1}{2} x^{T} H x

or a sparse linear function

c^{T} x

. If the objective function has already been defined, it will be overwritten. If handle_set_quadobj is called with no nonzeroes in either

c

H

, any existing objective function is removed, no new one is added and the problem will be solved as a feasible point problem. e04tef (no CPP interface) may be used to set individual elements

c_{i}

of the linear objective.

This objective function will typically be used for

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 problems (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)

or for Semidefinite Programming problems with bilinear matrix inequalities (BMI-SDP)

\begin{array}{l} \underset{x \in ℝ^{n}}{minimize} & \frac{1}{2} x^{T} H x + c^{T} x & (a) \\ subject to & \sum_{i,j = 1}^{n} x_{i} x_{j} Q_{i j}^{k} + \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}

(3)

The matrix

H

is a sparse symmetric

n \times n

matrix. It does not need to be positive definite. 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: $idxc (nnzc)$ – types::f77_integer array Input

On entry: the nonzero elements of the sparse vector

c

idxc (i - 1)

must contain the index of

c (i - 1)

in the vector, for

i = 1, 2, \dots, nnzc

. The elements must be stored in ascending order. Note that

n

is the current number of variables in the model.

Constraints:

$1 \leq idxc (i - 1) \leq n$ , for $i = 1, 2, \dots, nnzc$ ;
$idxc (i - 1) < idxc (i)$ , for $i = 1, 2, \dots, nnzc - 1$ .

3: $c (nnzc)$ – double array Input

On entry: the nonzero elements of the sparse vector

c

idxc (i - 1)

must contain the index of

c (i - 1)

in the vector, for

i = 1, 2, \dots, nnzc

. The elements must be stored in ascending order. Note that

n

is the current number of variables in the model.

Constraints:

$1 \leq idxc (i - 1) \leq n$ , for $i = 1, 2, \dots, nnzc$ ;
$idxc (i - 1) < idxc (i)$ , for $i = 1, 2, \dots, nnzc - 1$ .

4: $irowh (nnzh)$ – types::f77_integer array Input

On entry: arrays irowh, icolh and h store the nonzeros of the upper triangle of the matrix

H

in coordinate storage (CS) format (see Section 2.1.1 in the F11 Chapter Introduction). irowh specifies one-based row indices, icolh specifies one-based column indices and h specifies the values of the nonzero elements in such a way that

h_{i j} = h (l - 1)

where

i = irowh (l - 1)

j = icolh (l - 1)

, for

l = 1, 2, \dots, nnzh

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

Constraint:

1 \leq irowh (l - 1) \leq icolh (l - 1) \leq n

, for

l = 1, 2, \dots, nnzh

5: $icolh (nnzh)$ – types::f77_integer array Input

On entry: arrays irowh, icolh and h store the nonzeros of the upper triangle of the matrix

H

h_{i j} = h (l - 1)

where

i = irowh (l - 1)

j = icolh (l - 1)

, for

l = 1, 2, \dots, nnzh

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

Constraint:

1 \leq irowh (l - 1) \leq icolh (l - 1) \leq n

, for

l = 1, 2, \dots, nnzh

6: $h (nnzh)$ – double array Input

On entry: arrays irowh, icolh and h store the nonzeros of the upper triangle of the matrix

H

h_{i j} = h (l - 1)

where

i = irowh (l - 1)

j = icolh (l - 1)

, for

l = 1, 2, \dots, nnzh

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

Constraint:

1 \leq irowh (l - 1) \leq icolh (l - 1) \leq n

, for

l = 1, 2, \dots, nnzh

7: $opt$ – OptionalE04RF Input/Output

Optional parameter container, derived from Optional.

5.1Additional Quantities

1: $nnzc$: The number of nonzero elements in the sparse vector $c$
2: $nnzh$: The number of nonzero elements in the upper triangle of the matrix $H$

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 right now, the solver is running.

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

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

$errorid = 7$: On entry, $i = ⟨ value ⟩$ , $idxc [i - 1] = ⟨ value ⟩$ and
$idxc [i + 0] = ⟨ value ⟩$ .
Constraint: $idxc [i - 1] < idxc [i + 0]$ (ascending order).

$errorid = 7$: On entry, $i = ⟨ value ⟩$ , $idxc [i - 1] = ⟨ value ⟩$ and
$n = ⟨ value ⟩$ .
Constraint: $1 \leq idxc [i - 1] \leq n$ .

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

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

$errorid = 8$: On entry, $i = ⟨ value ⟩$ , $irowh [i - 1] = ⟨ value ⟩$ and
$icolh [i - 1] = ⟨ value ⟩$ .
Constraint: $irowh [i - 1] \leq icolh [i - 1]$ (elements within the upper triangle).

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

$errorid = 10601$: 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_lp_ipm.

NAG Library Manual, Mark 27.1

Interfaces: FL CL CPP AD

NAG CPP Interface Introduction

E04 (Opt) Chapter Contents

e04rf: FL CL CPP AD

Namespace: nagcpp

Namespace: opt

Function: handle_set_quadobj

NAG CPP Interfacenagcpp::opt::handle_set_quadobj (e04rf)

▸▿ 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_quadobj (e04rf)