NAG Library Function Document

nag_opt_miqp_mps_write (e04mwc)

1  Purpose

2  Specification

3  Description

4  References

5  Arguments

1:    $\mathbf{fileid}$ – Nag_FileIDInput

On entry: the ID of the file to store the problem data as returned by a call to nag_open_file (x04acc).

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

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 and may be NULL. 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 may be NULL, 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 and may be NULL.

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 and may be NULL.

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

9:    $\mathbf{idxc}\left[\mathbf{nnzc}\right]$ – const IntegerInput

10:  $\mathbf{c}\left[\mathbf{nnzc}\right]$ – const doubleInput

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

The elements are stored in ascending order.

Constraints:

• $1\le \mathbf{idxc}\left[\mathit{i}-1\right]\le \mathbf{n}$, for $\mathit{i}=1,2,\dots ,\mathbf{nnzc}$;
• $\mathbf{idxc}\left[\mathit{i}-1\right]<\mathbf{idxc}\left[\mathit{i}\right]$, 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:  $\mathbf{a}\left[\mathbf{nnza}\right]$ – const doubleInput

13:  $\mathbf{irowa}\left[\mathbf{nnza}\right]$ – const IntegerInput

14:  $\mathbf{iccola}\left[\mathbf{n}+1\right]$ – const IntegerInput

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 and may be NULL.

Constraints:

• $1\le \mathbf{irowa}\left[\mathit{i}-1\right]\le \mathbf{m}$, for $\mathit{i}=1,2,\dots ,\mathbf{nnza}$;
• $\mathbf{iccola}\left[0\right]=1$;
• $\mathbf{iccola}\left[\mathit{i}-1\right]\le \mathbf{iccola}\left[\mathit{i}\right]$, for $\mathit{i}=1,2,\dots ,\mathbf{n}$;
• $\mathbf{iccola}\left[\mathbf{n}\right]=\mathbf{nnza}+1$.

15:  $\mathbf{bl}\left[\mathbf{n}+\mathbf{m}\right]$ – const doubleInput

16:  $\mathbf{bu}\left[\mathbf{n}+\mathbf{m}\right]$ – const doubleInput

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 $\mathbf{bl}\left[j-1\right]\le {-10}^{20}$; to specify a nonexistent upper bound, set $\mathbf{bu}\left[j-1\right]\ge {10}^{20}$.

Constraints:

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

17:  $\mathbf{pnames}\left[5\right]\left[9\right]$ – char Input

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 $127$).

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

$\mathbf{pnames}\left[0\right]$

Contains the name of the problem.

$\mathbf{pnames}\left[1\right]$

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 $\mathbf{pnames}\left[1\right]$ is not used.

$\mathbf{pnames}\left[2\right]$

Contains the name of the RHS set.

$\mathbf{pnames}\left[3\right]$

Contains the name of the RANGE.

$\mathbf{pnames}\left[4\right]$

Contains the name of the BOUNDS.

18:  $\mathbf{crname}\left[\mathbf{n}+\mathbf{m}\right]\left[9\right]$ – char Input

On exit: 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.

If $\mathbf{crname}\le 0$, crname is not referenced and may be NULL.

19:  $\mathbf{h}\left[\mathbf{nnzh}\right]$ – const doubleInput

20:  $\mathbf{irowh}\left[\mathbf{nnzh}\right]$ – const IntegerInput

21:  $\mathbf{iccolh}\left[\mathbf{ncolh}+1\right]$ – const IntegerInput

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 and may be NULL.

Constraints:

• $1\le \mathbf{irowh}\left[\mathit{i}-1\right]\le \mathbf{ncolh}$, for $\mathit{i}=1,2,\dots ,\mathbf{nnzh}$;
• $\mathbf{iccolh}\left[0\right]=1$;
• $\mathbf{iccolh}\left[\mathit{i}-1\right]\le \mathbf{iccolh}\left[\mathit{i}\right]$, for $\mathit{i}=1,2,\dots ,\mathbf{ncolh}$;
• $\mathbf{iccolh}\left[\mathbf{ncolh}\right]=\mathbf{nnzh}+1$.

22:  $\mathbf{minmax}$ – IntegerInput

On entry: minmax defines the direction of optimization problem.

$\mathbf{minmax}=-1$

Minimization.

$\mathbf{minmax}=1$

Maximization.

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

23:  $\mathbf{intvar}\left[\mathbf{lintvar}\right]$ – const IntegerInput

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 and may be NULL.

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

24:  $\mathbf{fail}$ – NagError *Input/Output

The NAG error argument (see Section 2.7 in How to Use the NAG Library and its Documentation).

6  Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.

NE_ARRAY_INPUT

On entry, $\mathbf{iccola}\left[0\right]=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{iccola}\left[0\right]=1$.

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

On entry, $\mathbf{iccolh}\left[0\right]=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{iccolh}\left[0\right]=1$.

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

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.

NE_BAD_PARAM

On entry, argument $〈\mathit{\text{value}}〉$ had an illegal value.

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

NE_BOUND

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

On entry, $j=〈\mathit{\text{value}}〉$, $\mathbf{bl}\left[\mathit{j}-1\right]=〈\mathit{\text{value}}〉$ and $\mathbf{bu}\left[\mathit{j}-1\right]=〈\mathit{\text{value}}〉$ are incorrect.
Constraint: $\mathbf{bl}\left[\mathit{j}-1\right]\le \mathbf{bu}\left[\mathit{j}-1\right]$.

On entry, $\mathit{j}=〈\mathit{\text{value}}〉$, $\mathbf{bl}\left[\mathit{j}-1\right]=〈\mathit{\text{value}}〉$ and $\mathbf{bu}\left[\mathit{j}-1\right]=〈\mathit{\text{value}}〉$, 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: $\mathbf{bl}\left[\mathit{j}-1\right]>\text{−1e+20}$, $\mathbf{bu}\left[\mathit{j}-1\right]<\text{1e+20}$.

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

NE_FILEID

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

NE_INT

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

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

NE_INT_2

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

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

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

NE_INT_3

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 $\mathbf{ncolh}>0$, $\mathbf{nnzh}>0$.

NE_INT_4

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.

NE_INTERNAL_ERROR

An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.

An unexpected error has been triggered by this function. Please contact NAG.
See Section 2.7.6 in How to Use the NAG Library and its Documentation for further information.

NE_INVALID_CS

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

On entry, $j=〈\mathit{\text{value}}〉$, $i=〈\mathit{\text{value}}〉$, $\mathbf{ncolh}=〈\mathit{\text{value}}〉$ and $\mathbf{irowh}\left[i-1\right]=〈\mathit{\text{value}}〉$
Constraint: $j\le \mathbf{irowh}\left[\mathit{i}-1\right]\le \mathbf{ncolh}$ (within the lower triangle).

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.

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.

NE_MPS_ILLEGAL_NAME

On entry, $\mathbf{crname}\left[\mathit{j}-1\right]$ for $j=〈\mathit{\text{value}}〉$ has been already used.
Constraint: the names in crname must be unique.

The name specified in $\mathbf{pnames}\left[1\right]$ is empty or has been already used among row names.
Constraint: the names in $\mathbf{pnames}\left[1\right]$ must be unique and nonempty if crname is provided and $\mathbf{nnzc}>0$.

NE_MPS_PRINTABLE

On entry, $\mathbf{crname}\left[\mathit{j}-1\right]$ for $j=〈\mathit{\text{value}}〉$ is incorrect.
Constraint: the names in crname must consist only of printable characters.

On entry, $\mathbf{pnames}\left[\mathit{j}-1\right]$ for $j=〈\mathit{\text{value}}〉$ is incorrect.
Constraint: the names in pnames must consist only of printable characters.

NE_NO_LICENCE

Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.

NE_NOT_INCREASING

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

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

NE_NOT_STRICTLY_INCREASING

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

NE_OBJ_BOUND

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

NE_STATE_VAL

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

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

NE_WRITE_ERROR

An error occurred when writing to file.

7  Accuracy

8  Parallelism and Performance

9  Further Comments

10  Example

10.1  Program Text

Program Text (e04mwce.c)

10.2  Program Data

Program Data (e04mwce.d)

10.3  Program Results

Program Results (e04mwce.r)