Unless specified otherwise, variables in a LINGO model default to being non-negative and continuous. More specifically, variables can assume any real value from zero to positive infinity. In many cases, this default domain for a variable may be inappropriate. For instance, you may want a variable to assume negative values, or you might want a variable restricted to purely integer values. LINGO provides nine variable domain functions, which allow you to override the default domain of a variable, and, in the case of @POSD, the domain of a matrix of variables. The names of these functions and a brief description of their usage are:
| @GIN | restricts a variable to being an integer value |
| @BIN | makes a variable binary (i.e., 0 or 1) |
| @FREE | allows a variable to assume any real value, positive or negative |
| @BND | limits a variable to fall within a finite range |
| @SOS | defines a set of binary variables and places restrictions on their collective values |
| @CARD | defines a set of binary variables and places an upper limit on their sum |
| @SEMIC | restricts variables to being either zero or greater-than a specified constant |
| @PRIORITY | used to assign branching priorities to variables. |
| @POSD | restricts a square matrix to being symmetric matrix and positive semi-definite |
| @ALLDIFF | requires a specified set of variables to taking on different integer values |
In the remainder of this section, we'll investigate the mechanics of using these functions, and present a number of examples illustrating their usage.
