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Re: [Help-glpk] a question about row dual value
From: |
Andrew Makhorin |
Subject: |
Re: [Help-glpk] a question about row dual value |
Date: |
Thu, 23 Oct 2008 03:26:39 +0300 |
> 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?