Re: [Help-glpk] a question about row dual value

[Andrew Makhorin]

> I have the following small question ( in cpx_lp form )


> ====================

> Minimize
>  obj: + 0.191747629717657 x_1 + x_3

> Subject To
>  r_1: + x_2 - x_1 = 2
>  r_2: + x_3 + 0.216119012198317 x_2 >= 0.432238024396634

> Bounds
>  0 <= x_1 <= 1
>  -1 <= x_2 <= 2
>  x_3 free

>  

> End

> ================

> The row dual value for r_1 is 0, for which I have a question.

> In fact, when I change 2 to 1.99999, I get the dual value for r_1 is
> -0.191748 which I want.

Your lp has multiple optimal bases due to degeneracy. In one optimal
basis the constraint r_1: + x_2 - x_1 = 2 is non-active, so the
reduced cost of corresponding auxiliary (artificial) variable is zero.
Changing 2 to 1.99999 perturbs the instance and removes the degeneracy
(within a working precision).

> I know there is no solution when RHS of r_1 bigger than 2. But I
> am interested in the case that it is less than 2.

> I want to know if there is a way to get -0.191748 without
> changing the RHS value of r_1.

All optimal bases are equivalent in the sense that they all are optimal.
Why do you need to obtain a particular optimal basis?