NAG C Library Function Document

After the initialization function nag_opt_handle_init (e04rac) has been called, nag_opt_handle_set_linobj (e04rec) may be used to define the objective function of the problem as a linear function

c^{T} x

using a dense vector

c

unless the objective function has already been defined by another function 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 nag_opt_handle_set_quadobj (e04rfc) if the vector

c

is sparse. See nag_opt_handle_init (e04rac) for more details.

4

References

None.

5

Arguments

1: $handle$ – void *Input: On entry: the handle to the problem. It needs to be initialized by nag_opt_handle_init (e04rac) 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 nag_opt_handle_init (e04rac).
3: $cvec [nvar]$ – const doubleInput: On entry: the dense vector $c$ of the objective function.
4: $fail$ – NagError *Input/Output: The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

6

Error Indicators and Warnings

NE_ALLOC_FAIL: Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.
NE_ALREADY_DEFINED: The objective function has already been defined.
NE_BAD_PARAM: On entry, argument $〈value〉$ had an illegal value.
NE_HANDLE: 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 nag_opt_handle_init (e04rac) or it has been corrupted.
NE_INTERNAL_ERROR: An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 2.7.6 in How to Use the NAG Library and its Documentation for further information.
NE_NO_LICENCE: Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.
NE_PHASE: The problem cannot be modified in this phase any more, the solver has already been called.
NE_REF_MATCH: On entry, $nvar = 〈value〉$ , expected $value = 〈value〉$ .
Constraint: nvar must match the value given during initialization of handle.

7

Accuracy

Not applicable.

8

Parallelism and Performance

nag_opt_handle_set_linobj (e04rec) is not threaded in any implementation.

9

Further Comments

None.

10

Example

See Section 10 in nag_opt_handle_init (e04rac) for links to all the examples in the suite.

NAG C Library Manual, Mark 26

NAG Library Manual, Mark 26

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e04 Chapter Contents

e04 Chapter Introduction

NAG C Library Function Document

nag_opt_handle_set_linobj (e04rec)

▸▿ 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