e04mzf (qpconvex1_sparse_mps) : NAG Library, Mark 28

Old Code

mpslst = .False.    ! Or = .True.
Call e04mzf(infile,maxn,maxm,maxnnz,xbldef,xbudef,mpslst,n,m,nnz,iobj,   &
            ncolh,a,irowa,iccola,bl,bu,start,pnames,nname,crname,xs,     &
            istate,ifail)

if (ifail == 1 .Or. ifail == 2 .Or. ifail == 3) then
  ! not enough memory, allocate bigger arrays as given in m, n, nnz
  ! and call e04mzf again
else if (ifail >= 4 .And. ifail <= 16) then
  ! mps input file formating error
  ! stop
else if (ifail == 17) then
  ! wrong arguments to e04mzf
  ! stop
else if (ifail == 0) then
  ! data successfully read, call solver
end if

New Code

mpslst = 0      ! or = 1
Call e04mxf(infile,maxn,maxm,maxnnz,maxncolh,maxnnzh,maxlintvar,mpslst,  &
            n,m,nnz,ncolh,nnzh,lintvar,iobj,a,irowa,iccola,bl,bu,pnames, &
            nname,crname,h,irowh,iccolh,minmax,intvar,ifail)

if (ifail == 2) then
  ! not enough memory, allocate bigger arrays as given in m, n, nnz, ncolh,
  ! nnzh, lintvar and call e04mxf again
else if (ifail >= 3 .And. ifail <= 35) then
  ! MPS input file formatting error
  ! stop
else if (ifail == 36) then
  ! wrong input argument
  ! stop
else if (ifail=-999) then
  ! internal memory allocation error
  ! stop
else if (ifail == 0 .Or. ifail == 1) then
  ! data successfully read (with possible warning)
  start = 'C'
  do j=1,n
    xs(j) = min(max(0.0_nag_wp,bl(j)),bu(j))
    istate(j) = 0.0_nag_wp
  end do
  ! call solver
end if

1 Purpose

2 Specification

Fortran Interface

Subroutine e04mzf (

infile, maxn, maxm, maxnnz, xbldef, xbudef, mpslst, n, m, nnz, iobj, ncolh, a, ha, ka, bl, bu, start, names, nname, crname, xs, istate, ifail)

Integer, Intent (In)	::	infile, maxn, maxm, maxnnz
Integer, Intent (Inout)	::	ifail
Integer, Intent (Out)	::	n, m, nnz, iobj, ncolh, ha(maxnnz), ka(maxn+1), nname, istate(maxn+maxm)
Real (Kind=nag_wp), Intent (In)	::	xbldef, xbudef
Real (Kind=nag_wp), Intent (Out)	::	a(maxnnz), bl(maxn+maxm), bu(maxn+maxm), xs(maxn+maxm)
Logical, Intent (In)	::	mpslst
Character (1), Intent (Out)	::	start
Character (8), Intent (InOut)	::	names(5)
Character (8), Intent (Out)	::	crname(maxn+maxm)

C Header Interface

#include <nag.h>

void

e04mzf_ (const Integer *infile, const Integer *maxn, const Integer *maxm, const Integer *maxnnz, const double *xbldef, const double *xbudef, const logical *mpslst, Integer *n, Integer *m, Integer *nnz, Integer *iobj, Integer *ncolh, double a[], Integer ha[], Integer ka[], double bl[], double bu[], char *start, char names[], Integer *nname, char crname[], double xs[], Integer istate[], Integer *ifail, const Charlen length_start, const Charlen length_names, const Charlen length_crname)

C++ Header Interface

#include <nag.h>

extern "C" {

void

e04mzf_ (const Integer &infile, const Integer &maxn, const Integer &maxm, const Integer &maxnnz, const double &xbldef, const double &xbudef, const logical &mpslst, Integer &n, Integer &m, Integer &nnz, Integer &iobj, Integer &ncolh, double a[], Integer ha[], Integer ka[], double bl[], double bu[], char *start, char names[], Integer &nname, char crname[], double xs[], Integer istate[], Integer &ifail, const Charlen length_start, const Charlen length_names, const Charlen length_crname)

}

3 Description

e04mzf reads Linear Programming (LP) or Quadratic Programming (QP) problem data from an external file which is prepared in standard or compatible MPSX (see IBM (1971)) input format and then initializes

n

(the number of variables),

m

(the number of general linear constraints), the

m \times n

matrix

A

, and the vectors

l

u

and

c

(stored in row iobj of

A

) for use with e04nkf, which is designed to solve problems of the form

\underset{x \in R^{n}}{minimize} c^{T} x + \frac{1}{2} x^{T} H x subject to l \leq {\begin{matrix} x \\ A x \end{matrix}} \leq u .

For LP problems,

H = 0

. For QP problems, you must set

ncolh > 0

(see Section 5) and provide a subroutine to e04nkf to compute

H x

for any given vector

x

. The optional parameter Maximize may be used to specify an alternative problem in which the objective function is maximized (see Section 12.1 in e04nkf/e04nka).

The input file must not contain any blank lines. Any characters beyond column 80 are ignored. Indicator lines must not contain leading blank characters (in other words they must begin in column 1). The following displays the order in which the indicator lines must appear in the file:

NAME		user-supplied name
ROWS
	data line(s)
COLUMNS
	data line(s)
RHS
	data line(s)
RANGES		(optional)
	data line(s)
BOUNDS		(optional)
	data line(s)
ENDATA

A data line follows the same fixed format made up of fields defined below. The contents of the fields may have different significance depending upon the section of data in which they appear.

	Field 1	Field 2	Field 3	Field 4	Field 5	Field 6
Columns	$2 - 3$	$5 - 12$	$15 - 22$	$25 - 36$	$40 - 47$	$50 - 61$
Contents	Code	Name	Name	Value	Name	Value

The names and codes consist of ‘alphanumeric’ characters (i.e., a–z, A–Z,

0

–

9

+

-

*

, blank ( ), :, $ or full stop (.) only) and the names must not contain leading blank characters. Values are read using Fortran format

E12.0

. This allows values to be entered in several equivalent forms. For example,

1.2345678

1.2345678E+0

123.45678E−2

and

12345678E−07

all represent the same number. It is safest to include an explicit decimal point.

Note that in order to ensure numeric values are interpreted as intended, they should be right-justified in the

12

-character field, with no trailing blanks. This is because in some situations trailing blanks may be interpreted as zeros and this can dramatically affect the interpretation of the value. This is relevant if the value contains an exponent, or if it contains neither an exponent nor an explicit decimal point. For example, the fields

%%%%1.23E-2%
%%%%%%%123%%

may be interpreted as

1.23E−20

and

12300

respectively (where % denotes a blank). The actual behaviour is system-dependent.

Columns outside the six fields must be blank, except for columns 72–80, whose contents are ignored by the routine. These columns may be used to enter a sequence number. A non-blank character outside the predefined six fields and columns 72–80 is considered to be a major error (

ifail = 13

; see Section 6), unless it is part of a comment.

These lines specify row (constraint) names and their inequality types (i.e.,

=

\geq

\leq

Field 1:

defines the constraint type. It may be in column 2 or column 3.

N	free row, that is no constraint. It may be used to define the objective row.
G	greater than or equal to (i.e., $\geq$ ).
L	less than or equal to (i.e., $\leq$ ).
E	exactly equal to (i.e., $=$ ).

Field 2:

defines the row name.

Row type N stands for ‘Not binding’, also known as ‘Free’. It can be used to define the objective row. The objective row is a free row that specifies the vector

c

in the linear objective term

c^{T} x

. It is taken to be the first free row, unless some other free row name is specified by the names array (see Section 5). Note that

c

is assumed to be zero if (for example) the line

%N%%DUMMYROW

(where % denotes a blank) appears in the ROWS section of the MPSX data file, and the row name DUMMYROW is omitted from the COLUMNS section.

These lines specify the names to be assigned to the variables (columns) in the general linear constraint matrix

A

, and define, in terms of column vectors, the actual values of the corresponding matrix elements.

Field 1:	blank (ignored).
Field 2:	gives the name of the column associated with the elements specified in the following fields.
Field 3:	contains the name of a row.
Field 4:	used in conjunction with Field 3 contains the value of the matrix element.
Field 5:	is optional (may be used like Field 3).
Field 6:	is optional (may be used like Field 4).

Note that only the nonzero elements of

A

and

c

need to be specified in the COLUMNS section, as any zero elements of

A

are removed and any unspecified elements of

c

are assumed to be zero. In addition, any nonzero elements in the

j

th column of

A

must be grouped together before those in the

(j + 1)

th column, for

j = 1, 2, \dots, n - 1

. Nonzero elements within a column may however appear in any order.

This section specifies the right-hand side values of the general linear constraint matrix

A

(if any). The lines specify the name to be given to the right-hand side (RHS) vector along with the numerical values of the elements of the vector, which may appear in any order. The data lines have exactly the same format as the COLUMNS data lines, except that the column name is replaced by the RHS name. Only the nonzero elements need be specified. Note that this section may be empty, in which case the RHS vector is assumed to be zero.

Ranges are used for constraints of the form

l \leq A x \leq u

, where both

l

and

u

are finite. The range of the constraint is

r = u - l

. Either

l

u

must be specified in the RHS section and

r

must be defined in this section. The data lines have exactly the same format as the COLUMNS data lines, except that the column name is replaced by the RANGES name.

These lines specify limits on the values of the variables (

l

and

u

l \leq x \leq u

). If the variable is not specified in the bound set then it is automatically assumed to lie between default lower and upper bounds (usually

0

and

+ \infty

). Like an RHS column which is given a name, the set of variables in one bound set is also given a name.

Field 1:

specifies the type of bound or defines the variable type.

LO	lower bound
UP	upper bound
FX	fixed variable
FR	free variable ( $- \infty$ to $+ \infty$ )
MI	lower bound is $- \infty$
PL	upper bound is $+ \infty$ . This is the default variable type.

Field 2:

identifies a name for the bound set.

Field 3:

identifies the column name of the variable belonging to this set.

Field 4:

identifies the value of the bound; this has a numerical value only in association with LO, UP, FX in Field 1, otherwise it is blank.

Field 5:

is blank and ignored.

Field 6:

is blank and ignored.

4 References

5 Arguments

6 Error Indicators and Warnings

Note: the error exits

ifail = 4

ifail = 16

are caused by having either a corrupt or a nonstandard MPSX data file. Refer to Section 3 for a detailed description of the MPSX format which can be read by e04mzf. If

mpslst = .TRUE.

, the last line of printed output refers to the line in the MPSX data file which contains the reported error.

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

minimize c^{T} x + \frac{1}{2} x^{T} H x subject to \begin{matrix} l & \leq A x & \leq u, \\ −2 & \leq x & \leq 2, \end{matrix}

where

c = (\begin{matrix} - 4.0 \\ - 1.0 \\ - 1.0 \\ - 1.0 \\ - 1.0 \\ - 1.0 \\ - 1.0 \\ - 0.1 \\ - 0.3 \end{matrix}), H = (\begin{matrix} 2 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 \\ 1 & 2 & 1 & 1 & 1 & 0 & 0 & 0 & 0 \\ 1 & 1 & 2 & 1 & 1 & 0 & 0 & 0 & 0 \\ 1 & 1 & 1 & 2 & 1 & 0 & 0 & 0 & 0 \\ 1 & 1 & 1 & 1 & 2 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \end{matrix}), ncolh = 5,

A = (\begin{matrix} 1.0 & 1.0 & 1.0 & 1.0 & 1.0 & 1.0 & 1.0 & 1.0 & 4.0 \\ 1.0 & 2.0 & 3.0 & 4.0 & - 2.0 & 1.0 & 1.0 & 1.0 & 1.0 \\ 1.0 & - 1.0 & 1.0 & - 1.0 & 1.0 & 1.0 & 1.0 & 1.0 & 1.0 \end{matrix}),

l = (\begin{matrix} - 2.0 \\ - 2.0 \\ - 2.0 \end{matrix}) and u = (\begin{matrix} 1.5 \\ 1.5 \\ 4.0 \end{matrix}) .

The optimal solution (to five figures) is

x^{*} = {(2.0, - 0.23333, - 0.26667, - 0.3, - 0.1, 2.0, 2.0, - 1.7777, - 0.45555)}^{T} .

Three bound constraints and two general linear constraints are active at the solution. Note that, although the Hessian matrix is positive semidefinite, the point

x^{*}

is unique.

NAG FL Interface
e04mzf (qpconvex1_sparse_mps)

Old Code

New Code

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results

NAG FL Interfacee04mzf (qpconvex1_​sparse_​mps)

Old Code

New Code

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results

NAG FL Interface
e04mzf (qpconvex1_sparse_mps)