unless the objective function has already been defined by another routine in the suite. This will typically be used for linear semidefinite programming problems (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}

(1)

or SDP with bilinear matrix inequalities (BMI-SDP) where the objective function has only linear terms. It is recommended to use e04rff if the vector

c

is sparse. See e04raf for more details.

4

References

None.

5

Arguments

1: $handle$ – Type (c_ptr)Input: On entry: the handle to the problem. It needs to be initialized by e04raf and must not be changed.
2: $nvar$ – IntegerInput: On entry: $n$ , the number of decision variables $x$ in the problem. It must be unchanged from the value set during the initialization of the handle by e04raf.
3: $cvec (nvar)$ – Real (Kind=nag_wp) arrayInput: On entry: the dense vector $c$ of the objective function.
4: $ifail$ – IntegerInput/Output: On entry: ifail must be set to $0$ , $- 1 or 1$ . If you are unfamiliar with this argument you should refer to Section 3.4 in How to Use the NAG Library and its Documentation for details.
For environments where it might be inappropriate to halt program execution when an error is detected, the value $- 1 or 1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, the recommended value is $- 1$ . 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 initialized by e04raf or it has been corrupted.

$ifail = 2$: The problem cannot be modified in this phase any more, the solver has already been called.

$ifail = 3$: The objective function has already been defined.

$ifail = 4$: On entry, $nvar = 〈value〉$ , expected $value = 〈value〉$ .
Constraint: nvar must match the value given during initialization of handle.

$ifail = - 99$: An unexpected error has been triggered by this routine. Please contact NAG.
See Section 3.9 in How to Use the NAG Library and its Documentation for further information.

$ifail = - 399$: Your licence key may have expired or may not have been installed correctly.
See Section 3.8 in How to Use the NAG Library and its Documentation for further information.

$ifail = - 999$: Dynamic memory allocation failed.
See Section 3.7 in How to Use the NAG Library and its Documentation for further information.

7

Accuracy

Not applicable.

8

Parallelism and Performance

e04ref is not threaded in any implementation.

9

Further Comments

None.

10

Example

See Section 10 in e04raf for links to all the examples in the suite.

e04ref (PDF version)

E04 (opt) Chapter Contents

E04 (opt) Chapter Introduction

NAG Library Manual

NAG Library Routine Document

e04ref (handle_set_linobj)

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

1

Purpose

2

Specification

3

Description