After the handle has been initialized (e.g., e04rac has been called), e04rec may be used to define the objective function of the problem as a linear function

c^{T} x

using a dense vector

c

. If the objective function has already been defined, it will be overwritten. If

c = 0

, any existing objective function is removed, no new one is added and the problem will be solved as a feasible point problem. It is recommended to use e04rfc if the vector

c

is sparse. e04tec may be used to set individual elements

c_{i}

of the linear objective.

This 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)

Second-order Cone Programming (SOCP)

\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) \\ x_{G^{i}} \in K^{m_{i}}, i = 1, \dots, r, & (d) \end{array}

(2)

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}

(3)

or SDP with bilinear matrix inequalities (BMI-SDP) where the objective function has only linear terms. See Section 4.1 in the E04 Chapter Introduction for more details about the NAG optimization modelling suite.

4 References

None.

5 Arguments

1: $handle$ – void * Input: On entry: the handle to the problem. It needs to be initialized (e.g., by e04rac) and must not be changed between calls to the NAG optimization modelling suite.
2: $nvar$ – Integer Input: On entry: $n$ , the current number of decision variables $x$ in the model.
3: $cvec [nvar]$ – const double Input: On entry: the dense vector $c$ of the objective function.
4: $fail$ – NagError * Input/Output: The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

NE_ALLOC_FAIL: Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
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 properly initialized 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 7.5 in the Introduction to the NAG Library CL Interface for further information.
NE_NO_LICENCE: Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.
NE_PHASE: The problem cannot be modified right now, the solver is running.
NE_REF_MATCH: On entry, $nvar = ⟨ value ⟩$ , expected $value = ⟨ value ⟩$ .
Constraint: nvar must match the current number of variables of the model in the handle.

7 Accuracy

Not applicable.

8 Parallelism and Performance

Background information to multithreading can be found in the Multithreading documentation.

e04rec is not threaded in any implementation.

9 Further Comments

9.1 Internal Changes

Internal changes have been made to this function as follows:

At Mark 27.1: Previously, it was not possible to modify the objective function once it was set or to edit the model once a solver had been called. These limitations have been removed and the associated error codes were removed.

For details of all known issues which have been reported for the NAG Library please refer to the Known Issues.