naginterfaces.library.opt.handle_​set_​linobj

naginterfaces.library.opt.handle_set_linobj(handle, cvec)

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

For full information please refer to the NAG Library document for e04re

https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/e04/e04ref.html

Parameters

handleHandle

The handle to the problem. It needs to be initialized (e.g., by handle_init()) and must not be changed between calls to the NAG optimization modelling suite.

cvecfloat, array-like, shape $\left(\text{nvar}\right)$

The dense vector $c$ of the objective function.

Raises

NagValueError

(errno $1$)

$handle$ has not been initialized.

(errno $1$)

$handle$ does not belong to the NAG optimization modelling suite, has not been initialized properly or is corrupted.

(errno $1$)

$handle$ has not been initialized properly or is corrupted.

(errno $2$)

The problem cannot be modified right now, the solver is running.

(errno $4$)

On entry, $\text{nvar}=⟨value⟩$, expected $value=⟨value⟩$.

Constraint: $\text{nvar}$ must match the current number of variables of the model in the $handle$.

Notes

After the $handle$ has been initialized (e.g., handle_init() has been called), handle_set_linobj 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 handle_set_quadobj() if the vector $c$ is sparse. handle_set_linobj_coeff() may be used to set individual elements $c_i$ of the linear objective.

This will typically be used for Linear Programming (LP)

$$\begin{array}{c}\begin{array}{ccc}{minimize}_{x\in R^n}& c^{T}x& \text{(a)}\\ \text{subject to}& l_B\le Bx\le u_B\text{,}& \text{(b)}\\ & l_x\le x\le u_x\text{,}& \text{(c)}\end{array}\end{array}$$

Second-order Cone Programming (SOCP)

$$\begin{array}{c}\begin{array}{ccc}{minimize}_{x\in R^n}& c^{T}x& \text{(a)}\\ \text{subject to}& l_B\le Bx\le u_B\text{,}& \text{(b)}\\ & l_x\le x\le u_x\text{,}& \text{(c)}\\ & x_{G^i}\in K^{m_i},i=1,\dots ,r\text{,}& \text{(d)}\end{array}\end{array}$$

linear Semidefinite Programming problems (SDP)

$$\begin{array}{c}\begin{array}{ccc}{minimize}_{x\in R^n}& c^{T}x& \text{(a)}\\ \text{subject to}& {\sum }_1^n{x}_i{A}_i^k-A_0^k⪰0\text{,}k=1,\dots ,m_A\text{,}& \text{(b)}\\ & l_B\le Bx\le u_B\text{,}& \text{(c)}\\ & l_x\le x\le u_x\text{,}& \text{(d)}\end{array}\end{array}$$

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

See also

naginterfaces.library.examples.opt.handle_add_vars_ex.main()

naginterfaces.library.examples.opt.handle_solve_pennon_bmi_ex.main()

naginterfaces.library.examples.opt.handle_solve_socp_ipm_ex.main()