QSopt MPS Format RHS and RANGES sections QSopt > Problem Formats > MPS Format
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By default "L", "G", and "E" constraints have a right-hand-side value of 0.0. If values other than 0.0 are needed, they are specified in the RHS and RANGES sections. The QSopt parser ignores all RHS and RANGES definitions for "N" constraints.

Field 1 in a RHS or RANGES data line is a (possibly empty) label. The parser ignores RHS and RANGES data lines with a label that differs from the label used in the section's first data line. (This convention makes it possible to study several different models with minimal change to the input; it arose in the days when data was described via card decks.)

RHS and RANGES data lines contain a row name on field 2, and a floating point value in field 3. Additional row name, number pairs may follow on fields 4 and 5, fields 6 and 7, etc. Each row may be mentioned at most once in a RHS data line, and at most once in a RANGES data line.

In the absence of a RANGES definition for a row, the row's right-hand-side either defaults to 0.0 or assumes the value given in its RHS data line. A constraint's RANGES definition states that the constraint's expression must evaluate to a number that falls within an interval that depends on the constraint's right-hand-side and the range value, as well as the constraint's sense. If rhs is a constraint's right-hand-side value and range is the constraint's range value, then the range interval is defined according to the following table:

sense interval
G [rhs, rhs + |range|]
L [rhs - |range|, rhs]
E [rhs, rhs + |range|]     if range ≥ 0 [rhs - |range|, rhs]     if range < 0
where |range| is range's absolute value.

The MPS input excerpt

            ROWS
              N  obj
              L  lower
              G  greater
              E  equal
            RHS 
              rhs lower 10
states that equal is equal to 0.0, greater is greater than or equal to 0.0, and lower is less than or equal to 10.0. Adding the lines
            RANGES 
              lower    8
              greater -5
              equal   -0.5
changes the constraints as to
  • lower's constraint expression falls inside the interval [2.0, 10.0]
  • greater's constraint expression falls inside the interval [0.0,5.0]
  • equal's constraint expression falls inside the interval [-0.5,0.0]

See also MPS format definition and MPS format sections.

 
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Last Updated: November 2003