naginterfaces.library.opt.handle_​set_​qconstr_​fac

naginterfaces.library.opt.handle_set_qconstr_fac(handle, s, mf, idqc, idxr=None, r=None, irowf=None, icolf=None, f=None)

handle_set_qconstr_fac is a part of the NAG optimization modelling suite and defines a new, or edits an existing, quadratic objective function or constraint of the problem using a factor of the quadratic coefficient matrix.

For full information please refer to the NAG Library document for e04rt

https://support.nag.com/numeric/nl/nagdoc_30/flhtml/e04/e04rtf.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.

sfloat

The constant term in quadratic constraint.

If $idqc=-1$, $s$ will not be referenced.

mfint

$m$, row dimension of matrix $F$.

idqcint

$idqc=0$

A new quadratic constraint is created.

$idqc>0$

Specifies the index of an existing constraint to be replaced. i.e., replaces the $idqc$th constraint.

$idqc=-1$

A new quadratic objective is created and will replace any previously defined objective function.

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

The nonzero elements of the sparse vector $r$. $idxr[i-1]$ must contain the index of $r[\text{i}-1]$ in the vector, for $\text{i}=1,2,\dots ,\text{nnzr}$. No particular order is expected, but elements should not repeat. Note that $n$ is the current number of variables in the problem.

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

The nonzero elements of the sparse vector $r$. $idxr[i-1]$ must contain the index of $r[\text{i}-1]$ in the vector, for $\text{i}=1,2,\dots ,\text{nnzr}$. No particular order is expected, but elements should not repeat. Note that $n$ is the current number of variables in the problem.

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

Arrays $irowf$, $icolf$ and $f$ store the nonzeros of the matrix $F$ in coordinate storage (CS) format (see the F11 Introduction). $irowf$ specifies one-based row indices, $icolf$ specifies one-based column indices and $f$ specifies the values of the nonzero elements in such a way that $F_{ij}=f[l-1]$ where $i=irowf[l-1]$, $j=icolf[\text{l}-1]$, for $\text{l}=1,2,\dots ,\text{nnzf}$. No particular order is expected, but elements should not repeat.

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

Arrays $irowf$, $icolf$ and $f$ store the nonzeros of the matrix $F$ in coordinate storage (CS) format (see the F11 Introduction). $irowf$ specifies one-based row indices, $icolf$ specifies one-based column indices and $f$ specifies the values of the nonzero elements in such a way that $F_{ij}=f[l-1]$ where $i=irowf[l-1]$, $j=icolf[\text{l}-1]$, for $\text{l}=1,2,\dots ,\text{nnzf}$. No particular order is expected, but elements should not repeat.

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

Arrays $irowf$, $icolf$ and $f$ store the nonzeros of the matrix $F$ in coordinate storage (CS) format (see the F11 Introduction). $irowf$ specifies one-based row indices, $icolf$ specifies one-based column indices and $f$ specifies the values of the nonzero elements in such a way that $F_{ij}=f[l-1]$ where $i=irowf[l-1]$, $j=icolf[\text{l}-1]$, for $\text{l}=1,2,\dots ,\text{nnzf}$. No particular order is expected, but elements should not repeat.

Returns

idqcint

If $idqc=0$ on entry, then $idqc$ is overwritten with the index of the new quadratic constraint. By definition, this is the number of quadratic constraints already defined plus one. Otherwise, $idqc$ stays unchanged.

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, $idqc=⟨value⟩$.

The given $idqc$ does not match with any quadratic constraint already defined.

(errno $5$)

On entry, $idqc=⟨value⟩$.

Constraint: $idqc\ge -1$.

(errno $6$)

On entry, $\text{nnzf}=⟨value⟩$.

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

(errno $6$)

On entry, $\text{nnzr}=⟨value⟩$.

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

(errno $6$)

On entry, $mf=⟨value⟩$.

Constraint: $mf>0$.

(errno $6$)

$\text{nnzr}$ and $\text{nnzf}$ cannot be zero at the same time.

(errno $7$)

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

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

(errno $7$)

On entry, more than one element of $idxr$ has index $⟨value⟩$.

Constraint: each element of $idxr$ must have a unique index.

(errno $8$)

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

Constraint: $1\le irowf[\text{i}-1]\le mf$.

(errno $8$)

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

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

(errno $8$)

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

Constraint: each element of $f$ must have a unique row and column index.

Notes

After the $handle$ has been initialized (e.g., handle_init() has been called), handle_set_qconstr_fac may be used to edit a model by adding or replacing a quadratic objective function or constraint of the form

$$\frac{1}{2}{x}^T{F}^{T}Fx+r^{T}x$$

and

$$\frac{1}{2}{x}^T{F}^{T}Fx+r^{T}x+s\le 0\text{,}$$

respectively.

The matrix $F$ is a sparse $m\times n$ matrix. It can be viewed as the factor of the symmetric matrix $Q=F^{T}F$ in a general quadratic function

$$\frac{1}{2}{x}^{T}Qx+r^{T}x+s\text{.}$$

It is also acceptable if $F$ is a zero matrix, in which case the corresponding objective function or constraint becomes linear. If you have the full matrix $Q$ as input data, please call function handle_set_qconstr() instead. Note that it is possible to temporarily disable and enable individual constraints in the model by handle_disable() and handle_enable(), respectively. See the E04 Introduction for more details about the NAG optimization modelling suite.