Bounds in LP file format

CPLEX conforms to these rules about bounds in the LP file format.

The optional bounds section in a file in LP format follows the mandatory constraint section. It is preceded by the word bounds or bound in any mix of lower- and uppercase characters.

Each bound definition must begin on a new line. The format for a bound is l_n  ≤x_n≤ u_n except in the following cases.

Upper and lower bounds may also be entered separately as

l_n ≤ x_n

x_n ≤ u_n

with the default lower bound of 0 (zero) and the default upper bound of +∞ remaining in effect until the bound is explicitly changed.

Bounds that fix a variable can be entered as simple equalities. For example, x5 = 5.6 is equivalent to 5.6 <= x5 <= 5.6.

The bounds +∞ (positive infinity) and -∞ (negative infinity) must be entered as words: +infinity, -infinity, +inf, -inf.

A variable with a negative infinity lower bound and positive infinity upper bound may be entered as free, in any mix of upper- and lowercase characters, with a space separating the variable name and the word free. For example, x7 free is equivalent to - infinity <= x7 <= + infinity .

The last bound entered takes precedence over previously entered bounds.