# NAG C Library Function Document

## 1Purpose

nag_opt_handle_set_linobj (e04rec) is a part of the NAG optimization modelling suite and defines the linear objective function of the problem.

## 2Specification

 #include #include
 void nag_opt_handle_set_linobj (void *handle, Integer nvar, const double cvec[], NagError *fail)

## 3Description

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 ${c}^{\mathrm{T}}x$ 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)
 $minimize x∈ℝn cTx (a) subject to ∑ i=1 n xi Aik - A0k ⪰ 0 , k=1,…,mA (b) lB≤Bx≤uB (c) lx≤x≤ux (d)$ (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.

None.

## 5Arguments

1:    $\mathbf{handle}$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:    $\mathbf{nvar}$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:    $\mathbf{cvec}\left[{\mathbf{nvar}}\right]$const doubleInput
On entry: the dense vector $c$ of the objective function.
4:    $\mathbf{fail}$NagError *Input/Output
The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

## 6Error 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.
The objective function has already been defined.
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 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, ${\mathbf{nvar}}=〈\mathit{\text{value}}〉$, expected $\mathrm{value}=〈\mathit{\text{value}}〉$.
Constraint: nvar must match the value given during initialization of handle.

Not applicable.

## 8Parallelism and Performance

nag_opt_handle_set_linobj (e04rec) is not threaded in any implementation.