NAG Library Routine Document

e04mwf (miqp_mps_write)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:     $\mathbf{outfile}$ – IntegerInput

On entry: the ID of the file to store the problem data as associated by a call to x04acf.

Constraint: $\mathbf{outfile}\ge 0$.

2:     $\mathbf{n}$ – IntegerInput

On entry: $n$, the number of variables in the problem.

Constraint: $\mathbf{n}\ge 1$.

3:     $\mathbf{m}$ – IntegerInput

On entry: $m$, 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).

Constraint: $\mathbf{m}\ge 0$.

4:     $\mathbf{nnzc}$ – IntegerInput

On entry: the number of nonzero elements in the sparse vector $c$.

If $\mathbf{nnzc}=0$, the vector $c$ is considered empty and the arrays idxc and c will not be referenced. In this case the linear term of the objective function, if any, might be provided via iobj.

Constraints:

• $\mathbf{nnzc}\ge 0$;
• if $\mathbf{nnzc}>0$, $\mathbf{iobj}=0$.

5:     $\mathbf{nnza}$ – IntegerInput

On entry: the number of nonzero elements in matrix $A$.

If $\mathbf{nnza}=0$, matrix $A$ is considered empty, arrays a and irowa will not be referenced, and iccola should be the array of $1$.

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

6:     $\mathbf{ncolh}$ – IntegerInput

On entry: the number of leading nonzero columns of the Hessian matrix $H$.

If $\mathbf{ncolh}=0$, 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.

Constraint: $0\le \mathbf{ncolh}\le \mathbf{n}$.

7:     $\mathbf{nnzh}$ – IntegerInput

On entry: the number of nonzero elements of the Hessian matrix $H$.

Constraints:

• if $\mathbf{ncolh}>0$, $\mathbf{nnzh}>0$;
• otherwise $\mathbf{nnzh}=0$.

8:     $\mathbf{lintvar}$ – IntegerInput

On entry: the number of integer variables in the problem.

If $\mathbf{lintvar}=0$, all variables are considered continuous and array intvar will not be referenced.

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

9:     $\mathbf{idxc}\left(\mathbf{nnzc}\right)$ – Integer arrayInput

10:   $\mathbf{c}\left(\mathbf{nnzc}\right)$ – Real (Kind=nag_wp) arrayInput

On entry: the nonzero elements of sparse vector $c$. $\mathbf{idxc}\left(\mathit{i}\right)$ must contain the index of $\mathbf{c}\left(\mathit{i}\right)$ in the vector, for $\mathit{i}=1,2,\dots ,\mathbf{nnzc}$.

The elements are stored in ascending order.

Constraints:

• $1\le \mathbf{idxc}\left(\mathit{i}\right)\le \mathbf{n}$, for $\mathit{i}=1,2,\dots ,\mathbf{nnzc}$;
• $\mathbf{idxc}\left(\mathit{i}\right)<\mathbf{idxc}\left(\mathit{i}+1\right)$, for $\mathit{i}=1,2,\dots ,\mathbf{nnzc}$.

11:   $\mathbf{iobj}$ – IntegerInput

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

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

Constraint: if $\mathbf{iobj}>0$, $\mathbf{nnzc}=0$.

12:   $\mathbf{a}\left(\mathbf{nnza}\right)$ – Real (Kind=nag_wp) arrayInput

13:   $\mathbf{irowa}\left(\mathbf{nnza}\right)$ – Integer arrayInput

14:   $\mathbf{iccola}\left(*\right)$ – Integer arrayInput

Note: the dimension of the array iccola must be at least $\mathbf{n}+1$ if $\mathbf{nnza}>0$.

On entry: the nonzero elements of matrix $A$ in compressed column storage (see Section 2.1.3 in the F11 Chapter 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 $\mathbf{nnza}=0$, a and irowa are not referenced.

Constraints:

• $1\le \mathbf{irowa}\left(\mathit{i}\right)\le \mathbf{m}$, for $\mathit{i}=1,2,\dots ,\mathbf{nnza}$;
• $\mathbf{iccola}\left(1\right)=1$;
• $\mathbf{iccola}\left(\mathit{i}\right)\le \mathbf{iccola}\left(\mathit{i}+1\right)$, for $\mathit{i}=1,2,\dots ,\mathbf{n}$;
• $\mathbf{iccola}\left(\mathbf{n}+1\right)=\mathbf{nnza}+1$.

15:   $\mathbf{bl}\left(\mathbf{n}+\mathbf{m}\right)$ – Real (Kind=nag_wp) arrayInput

16:   $\mathbf{bu}\left(\mathbf{n}+\mathbf{m}\right)$ – Real (Kind=nag_wp) arrayInput

On entry: 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 $\mathbf{bl}\left(j\right)\le {-10}^{20}$; to specify a nonexistent upper bound, set $\mathbf{bu}\left(j\right)\ge {10}^{20}$.

Constraints:

• $\mathbf{bl}\left(\mathit{j}\right)\le \mathbf{bu}\left(\mathit{j}\right)$, for $\mathit{j}=1,2,\dots ,\mathbf{n}+\mathbf{m}$;
• $\mathbf{bl}\left(\mathit{j}\right)<{10}^{20}$, for $\mathit{j}=1,2,\dots ,\mathbf{n}+\mathbf{m}$;
• $\mathbf{bu}\left(\mathit{j}\right)>-{10}^{20}$, for $\mathit{j}=1,2,\dots ,\mathbf{n}+\mathbf{m}$;
• if $\mathbf{iobj}>0$, $\mathbf{bl}\left(\mathbf{iobj}+\mathbf{n}\right)\le -{10}^{20}$ and $\mathbf{bu}\left(\mathbf{iobj}+\mathbf{n}\right)\ge {10}^{20}$.

17:   $\mathbf{pnames}\left(5\right)$ – Character(8) arrayInput

On entry: 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.

$\mathbf{pnames}\left(1\right)$

Contains the name of the problem.

$\mathbf{pnames}\left(2\right)$

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 $\mathbf{pnames}\left(2\right)$ is not used.

$\mathbf{pnames}\left(3\right)$

Contains the name of the RHS set.

$\mathbf{pnames}\left(4\right)$

Contains the name of the RANGE.

$\mathbf{pnames}\left(5\right)$

Contains the name of the BOUNDS.

18:   $\mathbf{nname}$ – IntegerInput

On entry: the number of column (i.e., variable) and row names supplied in the array crname.

If $\mathbf{nname}=0$, the names are automatically generated and the array crname is not referenced.

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

19:   $\mathbf{crname}\left(\mathbf{nname}\right)$ – Character(8) arrayInput

On entry: 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.

20:   $\mathbf{h}\left(\mathbf{nnzh}\right)$ – Real (Kind=nag_wp) arrayInput

21:   $\mathbf{irowh}\left(\mathbf{nnzh}\right)$ – Integer arrayInput

22:   $\mathbf{iccolh}\left(*\right)$ – Integer arrayInput

Note: the dimension of the array iccolh must be at least $\mathbf{ncolh}+1$ if $\mathbf{ncolh}>0$.

On entry: the nonzero elements of the Hessian matrix $H$ in compressed column storage (see Section 2.1.3 in the F11 Chapter 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 $\mathbf{ncolh}=0$, h is not referenced.

Constraints:

• $1\le \mathbf{irowh}\left(\mathit{i}\right)\le \mathbf{ncolh}$, for $\mathit{i}=1,2,\dots ,\mathbf{nnzh}$;
• $\mathbf{iccolh}\left(1\right)=1$;
• $\mathbf{iccolh}\left(\mathit{i}\right)\le \mathbf{iccolh}\left(\mathit{i}+1\right)$, for $\mathit{i}=1,2,\dots ,\mathbf{ncolh}$;
• $\mathbf{iccolh}\left(\mathbf{ncolh}+1\right)=\mathbf{nnzh}+1$.

23:   $\mathbf{minmax}$ – IntegerInput

On entry: minmax defines the direction of optimization problem.

$\mathbf{minmax}=-1$

Minimization.

$\mathbf{minmax}=1$

Maximization.

Constraint: $\mathbf{minmax}=-1$ or $1$.

24:   $\mathbf{intvar}\left(\mathbf{lintvar}\right)$ – Integer arrayInput

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

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

Constraint: $1\le \mathbf{intvar}\left(\mathit{j}\right)\le \mathbf{n}$, for $\mathit{j}=1,2,\dots ,\mathbf{lintvar}$.

25:   $\mathbf{ifail}$ – IntegerInput/Output

On entry: ifail must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this argument you should refer to Section 3.4 in How to Use the NAG Library and its Documentation for details.

For environments where it might be inappropriate to halt program execution when an error is detected, the value $-1\text{ or }1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this argument, the recommended value is $0$. When the value $-\mathbf{1}\text{ or }\mathbf{1}$ is used it is essential to test the value of ifail on exit.

On exit: $\mathbf{ifail}=\mathbf{0}$ unless the routine detects an error or a warning has been flagged (see Section 6).

6

Error Indicators and Warnings

$\mathbf{ifail}=1$

On entry, $\mathbf{outfile}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{outfile}\ge 0$.

$\mathbf{ifail}=2$

On entry, $\mathbf{m}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{m}\ge 0$.

On entry, $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{n}\ge 1$.

$\mathbf{ifail}=3$

On entry, $\mathbf{lintvar}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{lintvar}\ge 0$.

On entry, $\mathbf{nname}=〈\mathit{\text{value}}〉$, $\mathbf{n}=〈\mathit{\text{value}}〉$ and $\mathbf{m}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{nname}=0$ or $\mathbf{n}+\mathbf{m}$.

On entry, $\mathbf{nnza}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{nnza}\ge 0$.

On entry, $\mathbf{nnzc}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{nnzc}\ge 0$.

$\mathbf{ifail}=4$

On entry, $\mathbf{ncolh}=〈\mathit{\text{value}}〉$ and $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $0\le \mathbf{ncolh}\le \mathbf{n}$.

On entry, $\mathbf{ncolh}=〈\mathit{\text{value}}〉$ and $\mathbf{nnzh}=〈\mathit{\text{value}}〉$.
Constraint: if $\mathbf{ncolh}>0$, $\mathbf{nnzh}>0$.

On entry, $\mathbf{ncolh}=〈\mathit{\text{value}}〉$ and $\mathbf{nnzh}=〈\mathit{\text{value}}〉$.
Constraint: if $\mathbf{ncolh}=0$, $\mathbf{nnzh}=0$.

$\mathbf{ifail}=5$

On entry, $j=〈\mathit{\text{value}}〉$, $\mathbf{idxc}\left(\mathit{j}\right)=〈\mathit{\text{value}}〉$ and $\mathbf{idxc}\left(j+1\right)=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{idxc}\left(j\right)<\mathbf{idxc}\left(j+1\right)$.

On entry, $j=〈\mathit{\text{value}}〉$, $\mathbf{idxc}\left(\mathit{j}\right)=〈\mathit{\text{value}}〉$ and $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $1\le \mathbf{idxc}\left(\mathit{j}\right)\le \mathbf{n}$.

$\mathbf{ifail}=6$

On entry, $\mathbf{minmax}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{minmax}=-1$ or $1$.

$\mathbf{ifail}=7$

On entry, $\mathbf{iobj}=〈\mathit{\text{value}}〉$ and $\mathbf{m}=〈\mathit{\text{value}}〉$.
Constraint: $0\le \mathbf{iobj}\le \mathbf{m}$.

On entry, $\mathbf{iobj}=〈\mathit{\text{value}}〉$ and $\mathbf{nnzc}=〈\mathit{\text{value}}〉$.
Constraint: at most one of iobj or nnzc may be nonzero.

$\mathbf{ifail}=8$

On entry, $\mathbf{iobj}=〈\mathit{\text{value}}〉$, $\mathbf{bl}\left(\mathit{j}\right)=〈\mathit{\text{value}}〉$ and $\mathbf{bu}\left(\mathit{j}\right)=〈\mathit{\text{value}}〉$, if $\mathbf{iobj}>0$ the bounds must be infinite.
Constraints: $\mathbf{bl}\left(\mathit{j}\right)\le -\text{1E+20}$, $\mathbf{bu}\left(\mathit{j}\right)\ge \text{1E+20}$.

On entry, $\mathit{j}=〈\mathit{\text{value}}〉$, $\mathbf{bl}\left(\mathit{j}\right)=〈\mathit{\text{value}}〉$ and $\mathbf{bu}\left(\mathit{j}\right)=〈\mathit{\text{value}}〉$, the integer variable $\mathit{j}$ requires at least one bound finite.
Constraint: at least one of the following conditions must be met for integer variable j: $\mathbf{bl}\left(\mathit{j}\right)>\text{−1E+20}$, $\mathbf{bu}\left(\mathit{j}\right)<\text{1E+20}$.

On entry, $j=〈\mathit{\text{value}}〉$, $\mathbf{bl}\left(\mathit{j}\right)=〈\mathit{\text{value}}〉$ and $\mathbf{bu}\left(\mathit{j}\right)=〈\mathit{\text{value}}〉$ are incorrect.
Constraint: $\mathbf{bl}\left(\mathit{j}\right)\le \mathbf{bu}\left(\mathit{j}\right)$.

On entry, $j=〈\mathit{\text{value}}〉$ and $\mathbf{bl}\left(\mathit{j}\right)=〈\mathit{\text{value}}〉$, $\mathbf{bl}\left(\mathit{j}\right)$ is incorrect.
Constraint: $\mathbf{bl}\left(\mathit{j}\right)<\text{1E+20}$.

On entry, $j=〈\mathit{\text{value}}〉$ and $\mathbf{bu}\left(\mathit{j}\right)=〈\mathit{\text{value}}〉$, $\mathbf{bu}\left(\mathit{j}\right)$ is incorrect.
Constraint: $\mathbf{bu}\left(\mathit{j}\right)>-\text{1E+20}$.

$\mathbf{ifail}=9$

On entry, $\mathbf{crname}\left(\mathit{j}\right)$ for $j=〈\mathit{\text{value}}〉$ has been already used.
Constraint: the names in crname must be unique.

On entry, $\mathbf{crname}\left(\mathit{j}\right)$ for $j=〈\mathit{\text{value}}〉$ is incorrect.
Constraint: the names in crname must consist only of printable characters.

On entry, $\mathbf{pnames}\left(\mathit{j}\right)$ for $j=〈\mathit{\text{value}}〉$ is incorrect.
Constraint: the names in pnames must consist only of printable characters.

The name specified in $\mathbf{pnames}\left(2\right)$ is empty or has been already used among row names.
Constraint: the names in $\mathbf{pnames}\left(2\right)$ must be unique and nonempty if crname is provided and $\mathbf{nnzc}>0$.

$\mathbf{ifail}=10$

On entry, $\mathbf{intvar}\left(〈\mathit{\text{value}}〉\right)=\mathbf{intvar}\left(〈\mathit{\text{value}}〉\right)=$ $〈\mathit{\text{value}}〉$.
Constraint: all entries in intvar must be unique.

On entry, $j=〈\mathit{\text{value}}〉$, $\mathbf{intvar}\left(\mathit{j}\right)=〈\mathit{\text{value}}〉$ and $\mathbf{lintvar}=〈\mathit{\text{value}}〉$.
Constraint: $1\le \mathbf{intvar}\left(\mathit{j}\right)\le \mathbf{lintvar}$.

$\mathbf{ifail}=11$

On entry, $i=〈\mathit{\text{value}}〉$, $\mathbf{irowa}\left(\mathit{i}\right)=〈\mathit{\text{value}}〉$ and $\mathbf{m}=〈\mathit{\text{value}}〉$.
Constraint: $1\le \mathbf{irowa}\left(\mathit{i}\right)\le \mathbf{m}$.

On entry, more than one element of a has row index $〈\mathit{\text{value}}〉$ and column index $〈\mathit{\text{value}}〉$.
Constraint: each element of a must have a unique row and column index.

$\mathbf{ifail}=12$

On entry, $\mathbf{iccola}\left(1\right)=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{iccola}\left(1\right)=1$.

On entry, $\mathbf{iccola}\left(\mathbf{n}+1\right)=〈\mathit{\text{value}}〉$ and $\mathbf{nnza}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{iccola}\left(\mathbf{n}+1\right)=\mathbf{nnza}+1$.

On entry, $j=〈\mathit{\text{value}}〉$, $\mathbf{iccola}\left(\mathit{j}\right)=〈\mathit{\text{value}}〉$ and $\mathbf{iccola}\left(j+1\right)=〈\mathit{\text{value}}〉$, the values of iccola must be nondecreasing.
Constraint: $\mathbf{iccola}\left(\mathit{j}\right)\le \mathbf{iccola}\left(j+1\right)$.

$\mathbf{ifail}=13$

On entry, $j=〈\mathit{\text{value}}〉$, $i=〈\mathit{\text{value}}〉$, $\mathbf{ncolh}=〈\mathit{\text{value}}〉$ and $\mathbf{irowh}\left(i\right)=〈\mathit{\text{value}}〉$
Constraint: $j\le \mathbf{irowh}\left(\mathit{i}\right)\le \mathbf{ncolh}$ (within the lower triangle).

On entry, more than one element of h has row index $〈\mathit{\text{value}}〉$ and column index $〈\mathit{\text{value}}〉$.
Constraint: each element of h must have a unique row and column index.

$\mathbf{ifail}=14$

On entry, $\mathbf{iccolh}\left(1\right)=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{iccolh}\left(1\right)=1$.

On entry, $\mathbf{iccolh}\left(\mathbf{ncolh}+1\right)=〈\mathit{\text{value}}〉$ and $\mathbf{nnzh}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{iccolh}\left(\mathbf{ncolh}+1\right)=\mathbf{nnzh}+1$.

On entry, $j=〈\mathit{\text{value}}〉$, $\mathbf{iccolh}\left(\mathit{j}\right)=〈\mathit{\text{value}}〉$ and $\mathbf{iccolh}\left(j+1\right)=〈\mathit{\text{value}}〉$, the values of iccolh must be nondecreasing.
Constraint: $\mathbf{iccolh}\left(\mathit{j}\right)\le \mathbf{iccolh}\left(j+1\right)$.

$\mathbf{ifail}=15$

An error occurred when writing to file.

$\mathbf{ifail}=-99$

An unexpected error has been triggered by this routine. Please contact NAG.

See Section 3.9 in How to Use the NAG Library and its Documentation for further information.

$\mathbf{ifail}=-399$

Your licence key may have expired or may not have been installed correctly.

See Section 3.8 in How to Use the NAG Library and its Documentation for further information.

$\mathbf{ifail}=-999$

Dynamic memory allocation failed.

See Section 3.7 in How to Use the NAG Library and its Documentation for further information.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (e04mwfe.f90)

10.2

Program Data

Program Data (e04mwfe.d)

10.3

Program Results

Program Results (e04mwfe.r)