Re: [Help-glpk] Solving inequations

[Andrew Makhorin]

>I'm currently trying to solve a problem with inequations, but I'm from
>the area of algorithmic biology, so I don't know much about integer
>programming... Perhaps I can use glpk to solve it? The problem is:
>
>I want to find some x_i so that some inequations of the form
>
>c_0 + c_1 x_1 + ... >= 0
>
>hold. Also, all x_i are >= 0 and also have an upper limit. And all
>variables are integer, of course.
>
>So there's no optimizing going on actually, I just want to find any
>solution. Can this be formulated for glpk?
>
>I tried it by eliminationg variables, but the number of inequations
>grows too quickly. I have perhaps 20 x_i and 20 inequations.

Yes, you can use glpk to solve your problem.

You can try to describe your problem in GLPK/L modeling language (see
its description in the distribution) and then use the solver GLPSOL, or
you can use GLPK API routines (that assumes programming in C; see the
document "GLPK User's Guide" in the distribution).

In any case you should formulate your problem in the standard form and
specify zero objective function in order to find any integer feasible
solution (some examples in the documentation will help you). I think
there should be no troubles due to very small size of your problem.