COLUMNS

Normal MPS-style records of the form

column    row1    value1    [  row2    value2  ]

are supported. Non-linear relationships are modeled by using a formula instead of a constant in the value1 field. If a formula is used, then only one coefficient can be described in the record (that is, there can be no row2 value2). The formula begins with an equals sign ("=") and is as described in the previous section.

A formula must be contained entirely on one record. The maximum record length for files read by XSLPreadprob is 31000. Note that there are limits applied by the Optimizer to the lengths of the names of rows and columns.

Variables used in formulae may be included in the COLUMNS section as variables, or may exist only as items within formulae. A variable which exists only within formulae is called an implicit variable.

Sometimes the non-linearity cannot be written as a coefficient. For example, in the constraint
Y - LOG(X) = 0,
LOG(X) cannot be written in the form of a coefficient. In such a case, the reserved column name "=" may be used in the first field of the record as shown:

Y	MyRow	1
=	MyRow	= - LOG ( X )

Effectively, "=" is a column with a fixed activity of 1.0 .

When a file is read by XSLPreadprob, more than one coefficient can be defined for the same column/row intersection. As long as there is at most one constant coefficient (one not written as a formula), the coefficients will be added together. If there are two or more constant coefficients for the same intersection, they will be handled by the Optimizer according to its own rules (normally additive, but the objective function retains only the last coefficient).