[Help-glpk] Re: Feasibility in glpk?

[Andrew Makhorin]

> Thanks for your reply. Yes, I know the latest version is 4.32. But
> since version 4.8 has Java API provided by Bjoern
> (http://bjoern.dapnet.de/glpk/index.htm), my Java programs used the
> API.

> I tried other coefficients. It turns out for larger values, I got
> strange results as well. This may be because I'm trying to solve
> feasibility problem, so I modified my subject a bit.
> Below is an example of the feasibility problem (I don't need objective
> function. In my implementation, I use a fake objective function z = x1
> + x2):
> The LP is as follows:
> Maximize
> z = x1 + x2
> 0.04600662731785218 x1 - 1 x2 <= 0
> 0.0036805289240121435 x1 - 1 x2 <= 0
> 0.08833272571169222 x1  - 1 x2 <= 0
> x1 + x2 = 1

> We can see that (x1 = 0, x2 =1) is a feasible solution.
> The glpk tells me that the problem is feasible, but the values of x1
> and x2 are both 0, which contradicts with my constraint x1 + x2 = 1.

> I figured that if I change my problem to the follows, glpk works.
> Maximize
> z = x1 + x2
> 0.04600662731785218 x1 <= 0
> 0.0036805289240121435 x1 <= 0
> 0.08833272571169222 x1 <= 0
> x1 + x2 = 1

> glpk tells me that: (x1 = 0, x2 =1) is a feasible solution. This is
> what I expected.

> Can you explain why glpk gives me strange results in the first problem?

I cannot reproduce the error. In all cases I tried using various
options that might affect the mip solver the solution is the same:
x1 = 0 and x2 = 1. Could you include a call to lpx_print_mip and
lpx_write_mps and post me the output files corresponding to incorrect
solution? Thanks.

(If you are searching for an integer feasible solution, minimizing
the sum of infeasibilities would be more reasonable; see example model
sat.mod included in the glpk distribution.)