naginterfaces.library.opt.miqp_​mps_​write

naginterfaces.library.opt.miqp_mps_write(outfile, n, m, ncolh, iobj, bl, bu, pnames, crname, minmax, idxc=None, c=None, a=None, irowa=None, iccola=None, h=None, irowh=None, iccolh=None, intvar=None, io_manager=None)

miqp_mps_write writes data for sparse linear programming, mixed integer linear programming, quadratic programming or mixed integer quadratic programming problems to a file in MPS format.

For full information please refer to the NAG Library document for e04mw

https://support.nag.com/numeric/nl/nagdoc_30/flhtml/e04/e04mwf.html

Parameters

outfileint

The ID of the file to store the problem data as associated by a call to the FileObjManager method unit_from_fileobj().

nint

$n$, the number of variables in the problem.

mint

$m$, the number of constraints in the problem. This is the number of rows in the linear constraint matrix $A$, including the free row (if any; see $iobj$).

ncolhint

The number of leading nonzero columns of the Hessian matrix $H$.

If $ncolh=0$, the quadratic term $H$ of the objective function is considered zero (e.g., LP problems), and arrays $h$, $irowh$ and $iccolh$ will not be referenced.

iobjint

If $iobj>0$, row $iobj$ of $A$ is a free row containing the nonzero coefficients of the linear terms of the objective function. In this case $\text{nnzc}$ is set to $0$.

If $iobj=0$, there is no free row in $A$, and the linear terms might be supplied in array $c$.

blfloat, array-like, shape $(n+m)$

$bl$ and $bu$ contains the lower bounds $l$ and the upper bounds $u$, respectively.

The first $n$ elements refer to the bounds for the variables $x$ and the rest to the bounds for the linear constraints (including the objective row $iobj$ if present).

To specify a nonexistent lower bound (i.e., $l_j=-inf$), set $bl[j-1]\le -{10}^{20}$; to specify a nonexistent upper bound, set $bu[j-1]\ge {10}^{20}$.

bufloat, array-like, shape $(n+m)$

$bl$ and $bu$ contains the lower bounds $l$ and the upper bounds $u$, respectively.

The first $n$ elements refer to the bounds for the variables $x$ and the rest to the bounds for the linear constraints (including the objective row $iobj$ if present).

To specify a nonexistent lower bound (i.e., $l_j=-inf$), set $bl[j-1]\le -{10}^{20}$; to specify a nonexistent upper bound, set $bu[j-1]\ge {10}^{20}$.

pnamesstr, length 8, array-like, shape $\left(5\right)$

A set of names associated with the MPSX form of the problem.

The names can be composed only from ‘printable’ characters (ASCII codes between $32$ and $126$).

If any of the names are blank, the default name is used.

$pnames\left[0\right]$

Contains the name of the problem.

$pnames\left[1\right]$

Contains the name of the objective row if the objective is provided in $c$ instead of $iobj$ and all names $crname$ are given. The name must be nonempty and unique. In all other cases $pnames\left[1\right]$ is not used.

$pnames\left[2\right]$

Contains the name of the RHS set.

$pnames\left[3\right]$

Contains the name of the RANGE.

$pnames\left[4\right]$

Contains the name of the BOUNDS.

crnamestr, length 8, array-like, shape $\left(\text{nname}\right)$

The names of all the variables and constraints in the problem in that order.

The names can be composed only from ‘printable’ characters and must be unique.

minmaxint

$minmax$ defines the direction of optimization problem.

$minmax=-1$

Minimization.

$minmax=1$

Maximization.

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

The nonzero elements of sparse vector $c$. $idxc[\text{i}-1]$ must contain the index of $c[\text{i}-1]$ in the vector, for $\text{i}=1,2,\dots ,\text{nnzc}$.

The elements are stored in ascending order.

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

The nonzero elements of sparse vector $c$. $idxc[\text{i}-1]$ must contain the index of $c[\text{i}-1]$ in the vector, for $\text{i}=1,2,\dots ,\text{nnzc}$.

The elements are stored in ascending order.

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

The nonzero elements of matrix $A$ in compressed column storage (see the F11 Introduction). Arrays $irowa$ and $a$ store the row indices and the values of the nonzero elements, respectively. The elements are sorted by columns and within each column in nondecreasing order. Duplicate entries are not allowed. $iccola$ contains the (one-based) indices to the beginning of each column in $a$ and $irowa$.

If $\text{nnza}=0$, $a$ and $irowa$ are not referenced.

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

The nonzero elements of matrix $A$ in compressed column storage (see the F11 Introduction). Arrays $irowa$ and $a$ store the row indices and the values of the nonzero elements, respectively. The elements are sorted by columns and within each column in nondecreasing order. Duplicate entries are not allowed. $iccola$ contains the (one-based) indices to the beginning of each column in $a$ and $irowa$.

If $\text{nnza}=0$, $a$ and $irowa$ are not referenced.

iccolaNone or int, array-like, shape $(:)$, optional

Note: the required length for this argument is determined as follows: if $\text{nnza}>0$: $n+1$; otherwise: $0$.

The nonzero elements of matrix $A$ in compressed column storage (see the F11 Introduction). Arrays $irowa$ and $a$ store the row indices and the values of the nonzero elements, respectively. The elements are sorted by columns and within each column in nondecreasing order. Duplicate entries are not allowed. $iccola$ contains the (one-based) indices to the beginning of each column in $a$ and $irowa$.

If $\text{nnza}=0$, $a$ and $irowa$ are not referenced.

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

The nonzero elements of the Hessian matrix $H$ in compressed column storage (see the F11 Introduction). The Hessian matrix, $H$, is symmetric and its elements are stored in a lower triangular matrix.

Arrays $irowh$ and $h$ store the row indices and the values of the nonzero elements, respectively.

The elements are sorted by columns and within each column in nondecreasing order.

Duplicate entries are not allowed. $iccolh$ contains the (one-based) indices to the beginning of each column in $h$ and $irowh$.

If $ncolh=0$, $h$ is not referenced.

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

The nonzero elements of the Hessian matrix $H$ in compressed column storage (see the F11 Introduction). The Hessian matrix, $H$, is symmetric and its elements are stored in a lower triangular matrix.

Arrays $irowh$ and $h$ store the row indices and the values of the nonzero elements, respectively.

The elements are sorted by columns and within each column in nondecreasing order.

Duplicate entries are not allowed. $iccolh$ contains the (one-based) indices to the beginning of each column in $h$ and $irowh$.

If $ncolh=0$, $irowh$ is not referenced.

iccolhNone or int, array-like, shape $(:)$, optional

Note: the required length for this argument is determined as follows: if $ncolh>0$: $ncolh+1$; otherwise: $0$.

The nonzero elements of the Hessian matrix $H$ in compressed column storage (see the F11 Introduction). The Hessian matrix, $H$, is symmetric and its elements are stored in a lower triangular matrix.

Arrays $irowh$ and $h$ store the row indices and the values of the nonzero elements, respectively.

The elements are sorted by columns and within each column in nondecreasing order.

Duplicate entries are not allowed. $iccolh$ contains the (one-based) indices to the beginning of each column in $h$ and $irowh$.

If $ncolh=0$, $iccolh$ is not referenced.

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

$intvar$ contains the indices $k$ of variables $x_k$ which are defined as integers. Duplicate indices are not allowed.

If $\text{lintvar}=0$, $intvar$ is not referenced.

io_managerFileObjManager, optional

Manager for I/O in this routine.

Raises

NagValueError

(errno $1$)

On entry, $outfile=⟨value⟩$.

Constraint: $outfile\ge 0$.

(errno $2$)

On entry, $n=⟨value⟩$.

Constraint: $n\ge 1$.

(errno $2$)

On entry, $m=⟨value⟩$.

Constraint: $m\ge 0$.

(errno $3$)

On entry, $\text{nnzc}=⟨value⟩$.

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

(errno $3$)

On entry, $\text{nnza}=⟨value⟩$.

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

(errno $3$)

On entry, $\text{lintvar}=⟨value⟩$.

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

(errno $3$)

On entry, $\text{nname}=⟨value⟩$, $n=⟨value⟩$ and $m=⟨value⟩$.

Constraint: $\text{nname}=0$ or $n+m$.

(errno $4$)

On entry, $ncolh=⟨value⟩$ and $n=⟨value⟩$.

Constraint: $0\le ncolh\le n$.

(errno $4$)

On entry, $ncolh=⟨value⟩$ and $\text{nnzh}=⟨value⟩$.

Constraint: if $ncolh>0$, $\text{nnzh}>0$.

(errno $4$)

On entry, $ncolh=⟨value⟩$ and $\text{nnzh}=⟨value⟩$.

Constraint: if $ncolh=0$, $\text{nnzh}=0$.

(errno $5$)

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

Constraint: $1\le idxc[\text{j}-1]\le n$.

(errno $5$)

On entry, $j=⟨value⟩$, $idxc[\text{j}-1]=⟨value⟩$ and $idxc\left[j\right]=⟨value⟩$.

Constraint: $idxc[j-1]<idxc\left[j\right]$.

(errno $6$)

On entry, $minmax=⟨value⟩$.

Constraint: $minmax=-1$ or $1$.

(errno $7$)

On entry, $iobj=⟨value⟩$ and $m=⟨value⟩$.

Constraint: $0\le iobj\le m$.

(errno $7$)

On entry, $iobj=⟨value⟩$ and $\text{nnzc}=⟨value⟩$.

Constraint: at most one of $iobj$ or $\text{nnzc}$ may be nonzero.

(errno $8$)

On entry, $j=⟨value⟩$, $bl[\text{j}-1]=⟨value⟩$ and $bu[\text{j}-1]=⟨value⟩$ are incorrect.

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

(errno $8$)

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

Constraint: $bl[\text{j}-1]<1e+20$.

(errno $8$)

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

Constraint: $bu[\text{j}-1]>-1e+20$.

(errno $8$)

On entry, $iobj=⟨value⟩$, $bl[\text{j}-1]=⟨value⟩$ and $bu[\text{j}-1]=⟨value⟩$, if $iobj>0$ the bounds must be infinite.

Constraints: $bl[\text{j}-1]\le -1e+20$, $bu[\text{j}-1]\ge 1e+20$.

(errno $8$)

On entry, $\text{j}=⟨value⟩$, $bl[\text{j}-1]=⟨value⟩$ and $bu[\text{j}-1]=⟨value⟩$, the integer variable $\text{j}$ requires at least one bound finite.

Constraint: at least one of the following conditions must be met for integer variable j: $bl[\text{j}-1]>-1e+20$, $bu[\text{j}-1]<1e+20$.

(errno $9$)

On entry, $crname[\text{j}-1]$ for $j=⟨value⟩$ is incorrect.

Constraint: the names in $crname$ must consist only of printable characters.

(errno $9$)

On entry, $pnames[\text{j}-1]$ for $j=⟨value⟩$ is incorrect.

Constraint: the names in $pnames$ must consist only of printable characters.

(errno $9$)

On entry, $crname[\text{j}-1]$ for $j=⟨value⟩$ has been already used.

Constraint: the names in $crname$ must be unique.

(errno $9$)

The name specified in $pnames\left[1\right]$ is empty or has been already used among row names.

Constraint: the names in $pnames\left[1\right]$ must be unique and nonempty if $crname$ is provided and $\text{nnzc}>0$.

(errno $10$)

On entry, $j=⟨value⟩$, $intvar[\text{j}-1]=⟨value⟩$ and $\text{lintvar}=⟨value⟩$.

Constraint: $1\le intvar[\text{j}-1]\le \text{lintvar}$.

(errno $10$)

On entry, $intvar[⟨value⟩]=intvar[⟨value⟩]=$ $⟨value⟩$.

Constraint: all entries in $intvar$ must be unique.

(errno $11$)

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

Constraint: $1\le irowa[\text{i}-1]\le m$.

(errno $11$)

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

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

(errno $12$)

On entry, $j=⟨value⟩$, $iccola[\text{j}-1]=⟨value⟩$ and $iccola\left[j\right]=⟨value⟩$, the values of $iccola$ must be nondecreasing.

Constraint: $iccola[\text{j}-1]\le iccola\left[j\right]$.

(errno $12$)

On entry, $iccola\left[0\right]=⟨value⟩$.

Constraint: $iccola\left[0\right]=1$.

(errno $12$)

On entry, $iccola\left[n\right]=⟨value⟩$ and $\text{nnza}=⟨value⟩$.

Constraint: $iccola\left[n\right]=\text{nnza}+1$.

(errno $13$)

On entry, $j=⟨value⟩$, $i=⟨value⟩$, $ncolh=⟨value⟩$ and $irowh[\text{i}-1]=⟨value⟩$

Constraint: $j\le irowh[\text{i}-1]\le ncolh$ (within the lower triangle).

(errno $13$)

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

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

(errno $14$)

On entry, $j=⟨value⟩$, $iccolh[\text{j}-1]=⟨value⟩$ and $iccolh\left[j\right]=⟨value⟩$, the values of $iccolh$ must be nondecreasing.

Constraint: $iccolh[\text{j}-1]\le iccolh\left[j\right]$.

(errno $14$)

On entry, $iccolh\left[0\right]=⟨value⟩$.

Constraint: $iccolh\left[0\right]=1$.

(errno $14$)

On entry, $iccolh\left[ncolh\right]=⟨value⟩$ and $\text{nnzh}=⟨value⟩$.

Constraint: $iccolh\left[ncolh\right]=\text{nnzh}+1$.

(errno $15$)

An error occurred when writing to file.

Notes

miqp_mps_write writes data for Linear Programming (LP) or Quadratic Programming (QP) problems (or their mixed integer variants) from an optimization problem to a MPS output file, see MPS Input Format for miqp_mps_read for the format description. The problem is expected in the form

$$\begin{array}{c}{minimize}_x\left(c^{T}x+\frac{1}{2}{x}^{T}Hx\right)\text{subject to}l\le \left\{\begin{array}{c}x\\ Ax\end{array}\right\}\le u\text{.}\end{array}$$

Where $n$ is the number of variables, $m$ is the number of general linear constraints, $A$ is the linear constraint matrix with dimension $m\times n$, the vectors $l$ and $u$ are the lower and upper bounds, respectively. $H$ is the Hessian matrix with dimension $n\times n$, however, only leading $ncolh$ columns might contain nonzero elements and the rest is assumed to be zero.

Note that the linear term of the objective function $c$ might be supplied either as $c$ or via $iobj$. If $c$ is supplied then $idxc$ contains the indices of the nonzero elements of sparse vector $c$, whereas if $iobj$ is supplied ($iobj>0$), row $iobj$ of matrix $A$ is a free row storing the nonzero elements of $c$.

Note: that this function uses fixed MPS format, see IBM (1971).

References

IBM, 1971, MPSX – Mathematical programming system, Program Number 5734 XM4, IBM Trade Corporation, New York