[Help-glpk] Re: Specifying constraints with '<' instead of '<='

[Andrew Makhorin]

>What's the recommended way of specifying a constraint using 
>'less than' instead of 'less than or equal to'? It appears
>that only '<=' is available via lpx_set_col/row_bnds();

Constraints in the form of strict inequalities are not used in the
math programming. If a function h(x) is continuous in the neighborhood
of zero, the constraint h(x) > 0 is equivalent to h(x) >= 0 in the
sense that h(x) can approach to zero arbitrarily closely.

Note that if some variable is required to be integer (as in mip),
it, nevertheless, is treated as continuous, i.e. its integrality is an
additional, specific constraint included in the problem.

>Is it legit to just subtract one from the RHS for integer
>problem?

You need to be careful when you meet something like x > 1, where x is
assumed to be integer. If you are sure that it is a strict inequality
(for example, if it is a negation of x <= 1), only then you can replace it
by x >= 2. In many cases that constraint may mean x >= 1.