naginterfaces.library.opt.handle_​set_​nlnconstr

naginterfaces.library.opt.handle_set_nlnconstr(handle, bl=None, bu=None, irowgd=None, icolgd=None)

handle_set_nlnconstr is a part of the NAG optimization modelling suite and defines or overwrites nonlinear constraints in the model, their number as well as the sparsity structure of their first derivatives.

For full information please refer to the NAG Library document for e04rk

https://support.nag.com/numeric/nl/nagdoc_30.2/flhtml/e04/e04rkf.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.

blNone or float, array-like, shape $\left(\text{ncnln}\right)$, optional

$bl$ and $bu$ define lower and upper bounds of the nonlinear constraints, $l_g$ and $u_g$, respectively. To define the $j$th constraint as equality, set $bl[j-1]=bu[j-1]=\beta$, where $\left|\beta \right|<\text{bigbnd}$. To specify a nonexistent lower bound (i.e., $l_j=-\infty$), set $bl[j-1]\le -\text{bigbnd}$; to specify a nonexistent upper bound, set $bu[j-1]\ge \text{bigbnd}$.

buNone or float, array-like, shape $\left(\text{ncnln}\right)$, optional

$bl$ and $bu$ define lower and upper bounds of the nonlinear constraints, $l_g$ and $u_g$, respectively. To define the $j$th constraint as equality, set $bl[j-1]=bu[j-1]=\beta$, where $\left|\beta \right|<\text{bigbnd}$. To specify a nonexistent lower bound (i.e., $l_j=-\infty$), set $bl[j-1]\le -\text{bigbnd}$; to specify a nonexistent upper bound, set $bu[j-1]\ge \text{bigbnd}$.

irowgdNone or int, array-like, shape $\left(\text{nnzgd}\right)$, optional

Arrays $irowgd$ and $icolgd$ store the sparsity structure (pattern) of the Jacobian matrix as $\text{nnzgd}$ nonzeros in coordinate storage (CS) format (see the F11 Introduction). The matrix has dimensions $\text{ncnln}\times n$. $irowgd$ specifies one-based row indices and $icolgd$ specifies one-based column indices. No particular order of elements is expected, but elements should not repeat and the same order should be used when the Jacobian is evaluated for the solver, e.g., the value of $\frac{\partial g_i}{\partial x_j}$ where $i=irowgd[l-1]$ and $j=icolgd[\text{l}-1]$ should be stored in $\text{gdx}[\text{l}-1]$ in $\text{congrd}$ in handle_solve_ipopt(), for $\text{l}=1,2,\dots ,\text{nnzgd}$.

icolgdNone or int, array-like, shape $\left(\text{nnzgd}\right)$, optional

Arrays $irowgd$ and $icolgd$ store the sparsity structure (pattern) of the Jacobian matrix as $\text{nnzgd}$ nonzeros in coordinate storage (CS) format (see the F11 Introduction). The matrix has dimensions $\text{ncnln}\times n$. $irowgd$ specifies one-based row indices and $icolgd$ specifies one-based column indices. No particular order of elements is expected, but elements should not repeat and the same order should be used when the Jacobian is evaluated for the solver, e.g., the value of $\frac{\partial g_i}{\partial x_j}$ where $i=irowgd[l-1]$ and $j=icolgd[\text{l}-1]$ should be stored in $\text{gdx}[\text{l}-1]$ in $\text{congrd}$ in handle_solve_ipopt(), for $\text{l}=1,2,\dots ,\text{nnzgd}$.

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 $6$)

On entry, $\text{nnzgd}=⟨value⟩$.

Constraint: $\text{nnzgd}>0$.

(errno $6$)

On entry, $\text{ncnln}=⟨value⟩$.

Constraint: $\text{ncnln}\ge 0$.

(errno $8$)

On entry, $i=⟨value⟩$, $irowgd[\text{i}-1]=⟨value⟩$ and $\text{ncnln}=⟨value⟩$.

Constraint: $1\le irowgd[\text{i}-1]\le \text{ncnln}$.

(errno $8$)

On entry, $i=⟨value⟩$, $icolgd[\text{i}-1]=⟨value⟩$ and $n=⟨value⟩$.

Constraint: $1\le icolgd[\text{i}-1]\le n$.

(errno $8$)

On entry, more than one element of structural Jacobian matrix has row index $⟨value⟩$ and column index $⟨value⟩$.

Constraint: each element of structural Jacobian matrix must have a unique row and column index.

(errno $10$)

On entry, $j=⟨value⟩$, $bl[j-1]=⟨value⟩$ and $bu[j-1]=⟨value⟩$.

Constraint: $bl[j-1]\le bu[j-1]$.

(errno $10$)

On entry, $j=⟨value⟩$, $bl[j-1]=⟨value⟩$, $\text{bigbnd}=⟨value⟩$.

Constraint: $bl[j-1]<\text{bigbnd}$.

(errno $10$)

On entry, $j=⟨value⟩$, $bu[j-1]=⟨value⟩$, $\text{bigbnd}=⟨value⟩$.

Constraint: $bu[j-1]>-\text{bigbnd}$.

Notes

After the $handle$ has been initialized (e.g., handle_init() has been called), handle_set_nlnconstr may be used to define the nonlinear constraints $l_g\le g\left(x\right)\le u_g$ of the problem. If the nonlinear constraints have already been defined, they will be overwritten and their Hessians (or the Hessian of the Lagrangian) will be removed. If handle_set_nlnconstr is called with $m_g=0$, existing nonlinear constraints are removed and no new ones are added. This will typically be used for nonlinear programming problems (NLP) of the kind:

$$\begin{array}{c}\begin{array}{ccc}{minimize}_{x\in R^n}& f\left(x\right)& \text{(a)}\\ \text{subject to}& l_g\le g\left(x\right)\le u_g\text{,}& \text{(b)}\\ & l_B\le Bx\le u_B\text{,}& \text{(c)}\\ & l_x\le x\le u_x\text{,}& \text{(d)}\end{array}\end{array}$$

where $n$ is the number of the decision variables $x$, $m_g$ is the number of the nonlinear constraints (in [equation](b)) and $g\left(x\right)$, $l_g$ and $u_g$ are $m_g$-dimensional vectors.

Note that upper and lower bounds are specified for all the constraints. This form allows full generality in specifying various types of constraint. In particular, the $j$th constraint may be defined as an equality by setting $l_j=u_j$. If certain bounds are not present, the associated elements $l_j$ or $u_j$ may be set to special values that are treated as $-\infty$ or $+\infty$. See the description of the option ‘Infinite Bound Size’ which is common among all solvers in the suite. Its value is denoted as $\text{bigbnd}$ further in this text. Note that the bounds are interpreted based on its value at the time of calling this function and any later alterations to ‘Infinite Bound Size’ will not affect these constraints.

Since each nonlinear constraint is most likely to involve a small subset of the decision variables, the partial derivatives of the constraint functions with respect to those variables are best expressed as a sparse Jacobian matrix of $m_g$ rows and $n$ columns. The row and column positions of all the nonzero derivatives must be registered with the handle through handle_set_nlnconstr. The values of the nonlinear constraint functions and their nonzero gradients at particular points in the decision variable space will be communicated to the NLP solver by user-supplied functions (e.g., $\text{confun}$ and $\text{congrd}$ for handle_solve_ipopt()).

An individual set of bounds can be also modified by handle_set_bound(). Note that it is also possible to temporarily disable and enable individual constraints in the model by calling handle_disable() and handle_enable(), respectively.

See the E04 Introduction for more details about the NAG optimization modelling suite.

See also

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

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