# NAG CL Interfacee04rec (handle_​set_​linobj)

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## 1Purpose

e04rec is a part of the NAG optimization modelling suite and defines or redefines the objective function of the problem to be linear.

## 2Specification

 #include
 void e04rec (void *handle, Integer nvar, const double cvec[], NagError *fail)
The function may be called by the names: e04rec or nag_opt_handle_set_linobj.

## 3Description

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 ${c}^{\mathrm{T}}x$ 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)
 $minimize x∈ℝn cTx (a) subject to lB≤Bx≤uB, (b) lx≤x≤ux , (c)$ (1)
Second-order Cone Programming (SOCP)
 $minimize x∈ℝn cTx (a) subject to lB≤Bx≤uB, (b) lx≤x≤ux , (c) xGi∈Kmi,i=1,…,r, (d)$ (2)
linear Semidefinite Programming problems (SDP)
 $minimize x∈ℝn cTx (a) subject to ∑ i=1 n xi Aik - A0k ⪰ 0 , k=1,…,mA , (b) lB≤Bx≤uB , (c) lx≤x≤ux , (d)$ (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.

None.

## 5Arguments

1: $\mathbf{handle}$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: $\mathbf{nvar}$Integer Input
On entry: $n$, the current number of decision variables $x$ in the model.
3: $\mathbf{cvec}\left[{\mathbf{nvar}}\right]$const double Input
On entry: the dense vector $c$ of the objective function.
4: $\mathbf{fail}$NagError * Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

## 6Error 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.
On entry, argument $⟨\mathit{\text{value}}⟩$ 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, ${\mathbf{nvar}}=⟨\mathit{\text{value}}⟩$, expected $\mathrm{value}=⟨\mathit{\text{value}}⟩$.
Constraint: nvar must match the current number of variables of the model in the handle.

Not applicable.

## 8Parallelism and Performance

e04rec is not threaded in any implementation.