Understanding solution answer: infeas??

[Banik]

Hi guys, I am new in GLPK use and I would like to ask you about some solution
that I get: Basically I define an LP problem where the variable x10, x11 and
x12 take values bw. 0 and 1 and the sum of x10+x11+x12 = 1, according to
that and for 18 structural variables I get the following answer:

> ./a.out                    
      0: obj =   0.000000000e+00  infeas =  6.000e+00 (0)
*     8: obj =   1.300000000e+03  infeas =  0.000e+00 (0)
*    13: obj =   1.600000000e+03  infeas =  8.171e-16 (0)
OPTIMAL SOLUTION FOUND

z = 1600
 x10 = 0; x11 = 0; x12 = 1
 x20 = 0; x21 = 0; x22 = 1
 x30 = 0; x31 = 0; x32 = 1
 x40 = 0; x41 = 0; x42 = 1
 x50 = 1; x51 = 0; x52 = -8.17124e-16
 x60 = 1; x61 = 0; x62 = 0

The value of z correspond to the right value, but how do I understand the
value of x52??, is it a real "0" value and how is it related to the "infeas
= 8.171e-16" value?, does it mean that my answer is wrong (since I should
have only expect x50 = 1; x51 = 0; x52 = 0)?

On advance thanks for the help you can give me!


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[Andrew Makhorin]

> Hi guys, I am new in GLPK use and I would like to ask you about some
> solution that I get: Basically I define an LP problem where the
> variable x10, x11 and x12 take values bw. 0 and 1 and the sum of
> x10+x11+x12 = 1, according to that and for 18 structural variables I
> get the following answer:

> ./a.out
>       0: obj =   0.000000000e+00  infeas =  6.000e+00 (0)
> *     8: obj =   1.300000000e+03  infeas =  0.000e+00 (0)
> *    13: obj =   1.600000000e+03  infeas =  8.171e-16 (0)
> OPTIMAL SOLUTION FOUND

> z = 1600
>  x10 = 0; x11 = 0; x12 = 1
>  x20 = 0; x21 = 0; x22 = 1
>  x30 = 0; x31 = 0; x32 = 1
>  x40 = 0; x41 = 0; x42 = 1
>  x50 = 1; x51 = 0; x52 = -8.17124e-16
>  x60 = 1; x61 = 0; x62 = 0

> The value of z correspond to the right value, but how do I understand
> the value of x52??, is it a real "0" value and how is it related to
> the "infeas = 8.171e-16" value?, does it mean that my answer is wrong
> (since I should have only expect x50 = 1; x51 = 0; x52 = 0)?

The solution is correct. You should understand x52 = -8.17124e-16 as
zero within a working precision. To perform calculations the glpk
simplex solver uses floating-point arithmetic, so it reports a solution,
which is an approximation to the mathematically exact result.



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