Reads an MPS file containing a linear programming problem or a quadratic programming problem.

Synopsis

#include <imsl.h>

imsl_f_mps* imsl_f_read_mps(char* filename, …, 0)

void imsl_f_free_mps(imsl_f_msp *mps)

The type double function is imsl_d_read_mps.

Required Argument

char* filename (Input)
Name of the MPS file to be read. It may be NULL if the optional argument IMSL_FILE is used.

Return Value

A pointer to a structure containing the data read from the MPS file. To release this space use imsl_f_free_mps.

The returned structure contains the following fields.

 

Field	Description
char* filename	Name of the MPS file.
char name[9]	Name of the problem.
int nrows	Number of rows in the constraint matrix.
int ncolumns	Number of columns in the constraint matrix. This is also the number of variables.
int nonzeros	Number of non-zeros in the constraint matrix.
int nhessian	Number of non-zeros in the Hessian matrix. If zero, then there is no Hessian matrix.
int ninteger	Number of variables required to be integer. This includes binary variables.
int nbinary	Number of variables required to be binary (0 or 1).
float* objective	A float array of length ncolumns containing the objective vector.
Imsl_f_sparse_elem* constraint	A imsl_f_sparse_elem array of length nonzeros containing the sparse matrix representation of the constraint matrix. See below for details.
Imsl_f_sparse_elem* hessian	A imsl_f_sparse_elem array of length nhessian containing the sparse matrix representation of the Hessian matrix. If nhessian is zero, then this field is NULL.
float* lower_range	A float array of length nrows containing the lower constraint bounds. If a constraint is unbounded below, the corresponding entry in lower_range is set to negative_infinity, defined below.
float* upper_range	A float array of length nrows containing the upper constraint bounds. If a constraint is unbounded above, the corresponding entry in upper_range is set to positive_infinity, defined below.
float* lower_bound	A float array of length ncolumns containing the lower variable bounds. If a variable is unbounded below, the corresponding entry in lower_bound is set to negative_infinity, defined below.
float* upper_bound	A float array of length ncolumns containing the upper variable bounds. If a variable is unbounded above, the corresponding entry in upper_bound is set to positive_infinity, defined below.
int* variable_type	An int array of length ncolumns containing the type of each variable. Variable types are:
	0	Continous
	1	Integer
	2	Binary (0 or 1)
	3	Semicontinuous
char name_objective[9]	Name of the set in ROWS used for the objective row.
char name_rhs[9]	Name of the RHS set used.
char name_ranges[9]	Name of the RANGES set used or the empty string if no RANGES section in the file.
char name_bounds[9]	Name of the BOUNDS set used or the empty string if no BOUNDS section in the file.
char** name_row	Array of length nrows containing the row names. The name of the i-th constraint row is name_row[i].
char** name_column	Array of length ncolumns containing the column names. The name of the i-th column and variable is name_column[i].
float positive_infinity	Value used for a constraint or bound upper limit when the constraint or bound is unbounded above. This can be set using an optional argument. Default is 1.0e+30.
float negative _infinity	Value used for a constraint or bound lower limit when the constraint or bound is unbounded below. This can be set using an optional argument. Default is -1.0e+30.

This structure stores the constraint and Hessian matrices in a simple sparse matrix format. For each non-zero element in the matrix, a row index, a column index and a value are given. The following code fragment expands the sparse constraint matrix in the structure pointed to by mps into a dense matrix:

 

/* allocate a matrix */

int nr = mps->nrows;

int nc = mps->ncolumns;

float* matrix = (float*)calloc(nr*nc, sizeof(float));

 

/* expand the sparse matrix */

for (k = 0;  k < mps->nonzeros;  k++) {

      i = mps->constraint[k].row;

      j = mps->constraint[k].col;

      matrix[nc*i+j] = mps->constraint[k].val;

}

 

Optional Arguments

IMSL_FILE, FILE, FILE* file, (Input)
Handle for MPS file. The file is read but not closed. This option overrides the filename required argument.

IMSL_NAME_RHS, char* name_rhs (Input)
Name of the RHS set to be used. An MPS file can contain multiple RHS sets.
By default, the first RHS set in the MPS file is used. This name is case sensitive.

IMSL_NAME_RANGES, char* name_ranges (Input)
Name of the RANGES set to be used. An MPS file can contain multiple RANGES sets.
By default, the first RANGES set in the MPS file is used. This name is case sensitive.

IMSL_NAME_BOUNDS, char* name_bounds (Input)
Name of the BOUNDS set to be used. An MPS file can contain multiple BOUNDS sets.
By default, the first BOUNDS set in the MPS file is used. This name is case sensitive.

IMSL_POSITIVE_INFINITY, float positive_infinity (Input)
Value used for a constraint or bound upper limit when the constraint or bound is unbounded above.
Default: 1.0e+30.

IMSL_NEGATIVE_INFINITY, float negative_infinity (Input)
Value used for a constraint or bound lower limit when the constraint or bound is unbounded below.
Default: -1.0e+30.

Description

An MPS file defines a linear or quadratic programming problem.

A linear programming problem is assumed to have the form:

A quadratic programming problem is assumed to have the form:

The following table maps this notation into the fields in the structure returned by the reader:

 

C	Objective
A	Constraint matrix
Q	Hessian matrix
	lower_range
	upper_range
	lower_bound
	upper_bound

If the MPS file specifies an equality constraint or bound, the corresponding lower and upper values in the returned structure will be exactly equal.

The problem formulation assumes that the constraints and bounds are two-sided. If a particular constraint or bound has no lower limit, then the corresponding entry in the structure is set to -1.0e+30. If the upper limit is missing, then the corresponding entry in the structure is set to +1.0e+30.

MPS File Format

There is some variability in the MPS format. This section describes the MPS format accepted by this reader.

An MPS file consists of a number of sections. Each section begins with a name in column 1. With the exception of the NAME section, the rest of this line is ignored. Lines with a ‘*’ or ‘$’ in column 1 are considered comment lines and are ignored.

The body of each section consists of lines divided into fields, as follows:

 

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

 

The format limits MPS names to 8 characters and values to 12 characters. The names in fields 2, 3 and 5 are case sensitive. Leading and trailing blanks are ignored, but internal spaces are significant.

 

The sections in an MPS file are as follows.

•      NAME

•      ROWS

•      COLUMNS

•      RHS

•      RANGES (optional)

•      BOUNDS (optional)

•      QUADRATIC (optional)

•      ENDATA

Sections must occur in the above order.

MPS keywords, section names and indicator values, are case insensitive. Row, column and set names are case sensitive.

NAME Section

The NAME section contains the single line. A problem name can occur anywhere on the line after NAME and before columns 62. The problem name is truncated to 8 characters.

ROWS Section

The ROWS section defines the name and type for each row. Field 1 contains the row type and field 2 contains the row name. Row type values are not case sensitive. Row names are case sensitive. The following row types allowed:

 

Row Type	Meaning
E	Equality Constraint.
L	Less than or equal constraint.
G	Greater than or equal constraint.
N	Objective or a free row.

COLUMNS Section

The COLUMNS section defines the nonzero entries in the objective and the constraint matrix. The row names here must have been defined in the ROWS section.

 

Field	Contents
2	Column name.
3	Row name.
4	Value for the entry whose row and column are given by fields.
5	Row name.
6	Value for the entry whose row and column are given by fields 5 and 2.

The COLUMNS section can also contain markers. These are indicated by the name ‘MARKER’ (with the quotes) in field 3 and the marker type in field 4 or 5.

Marker type ‘INTORG’ (with the quotes) begins an integer group. The marker type ‘INTEND’ (with the quotes) ends this group. The variables corresponding to the columns defined within this group are required to be integer.

RHS Section

The RHS section defines the right-hand side of the constraints. An MPS file can contain more than one RHS set, distinguished by the RHS set name. The row names here must be defined in the ROWS section.

Field	Contents
2	RHS set name.
3	Row name.
4	Value for the entry whose set and row are given by fields 2 and 3.
5	Row name.
6	Value for the entry whose set and row are given by fields 2 and 5.

RANGES Section

The optional RANGES section defines two-sided constraints. An MPS file can contain more than one range set, distinguished by the range set name. The row names here must have been defined in the ROWS section.

 

Field	Contents
2	Range set name.
3	Row name.
4	Value for the entry whose set and row are given by fields 2 and 3.
5	Row name.
6	Value for the entry whose set and row are given by fields 2 and 5.

 

Ranges change one-sided constraints, defined in the RHS section, into two-sided constraints. The two-sided constraint for row i depends on the range value, , defined in this section. The right-hand side value, , is defined in the RHS section. The two-sided constraints for row i are given in the following table:

 

Row Type	Lower Constraint	Upper Constraint
G
L
E

BOUNDS Section

The optional BOUNDS section defines bounds on the variables. By default, the bounds are. The bounds can also be used to indicate that a variable must be an integer.

More than one bound can be set for a single variable. For example, to set use a LO bound with value 2 to set and an UP bound with value 6 to add the condition.

An MPS file can contain more than one bounds set, distinguished by the bound set name.

 

Field	Contents
1	Bounds type.
2	Bounds set name.
3	Column name
4	Value for the entry whose set and column are given by fields 2 and 3.
5	Column name.
6	Value for the entry whose set and column are given by fields 2 and 5.

The bound types are as follows. Hereare the bound values defined in this section, the are the variables, and I is the set of integers.

Bounded Type	Definition	Formula
LO	Lower bound
UP	Upper bound
FX	Fixed variable
FR	Free variable
MI	Lower bound is minus infinity
PL	Upper bound is positive infinity
BV	Binary variable (variable must be 0 or 1).
UI	Upper bound and integer	and
LI	Lower bound and integer	and
SC	Semicontinuous	0 or

 

The bound type names are not case sensitive.

If the bound type is UP or UI and then the lower bound is set to.

QUADRATIC Section

The optional QUADRATIC section defines the Hessian for quadratic programming problems. The names HESSIAN, QUADS, QUADOBJ, QSECTION and QMATRIX are also recognized as beginning the QUADRATIC section.

 

 

Field	Contents
2	Column name.
3	Column name
4	Value for the entry whose row and column are given by fields 2 and 3.
5	Column name.
6	Value for the entry whose row and column are given by fields 2 and 4.

 

ENDATA Section

The ENDATA section ends the MPS file.

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