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Mathematical Optimization Procedures
 

The MPS-Format Data Table

QSECTION Section (Optional)

The QSECTION section is needed only to describe quadratic programming problems. It specifies the coefficients of the quadratic terms in the objective function.

  • Indicator record:

    _ID_ Field1 Field2 Field3 Field4 Field5 Field6
    Number QSECTION or QUADOBJ Blank Blank . Blank .

  • Data record:

    _ID_ Field1 Field2 Field3 Field4 Field5 Field6
    Number Blank Column name Column name Coefficient in objective function Blank .

Notes:

  1. The QSECTION section can appear only in PROC OPTQP and should not appear in PROC OPTLP or PROC OPTMILP. For PROC OPTLP and PROC OPTMILP, an error is reported when the submitted data table contains a QSECTION section. For PROC OPTQP, if the QSECTION section is not specified, or if there is no valid data record in the QSECTION section, then the LP solver is used to solve the resulting linear programming problem.

  2. The variables field2 and field3 contain the names of the columns that form a quadratic term in the objective function. They must have been defined in the COLUMNS section. They need not refer to the same column. Zero entries should not be specified.

  3. Duplicate entries of a quadratic term are not allowed. This means the combination of (field2, field3) must be unique, where left-parenthesis k comma j right-parenthesis and left-parenthesis j comma k right-parenthesis are considered to be the same combination.

  4. If field4 of one data record is missing or takes a value of zero, then this data record is ignored.

Last updated: June 22, 2026