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## Re: [Help-glpk] Specifying a constraint in CPLEX notation

 From: glpk xypron Subject: Re: [Help-glpk] Specifying a constraint in CPLEX notation Date: Thu, 04 Oct 2012 08:25:12 +0200

```Hello Reg,

which problems you can formulate does not depend on the input language to GLPK.
Using the GMPL language would make writing the input file much easier. See
glpk-4.47/doc/gmpl.pdf

> I want to constrain A[i] to be zero if all the B[i][j] in n are zero.
Checking if B[i][j] is zero will get you into trouble, if B[i,j] are not binary
or integer. Would you consider 1E-30 as zero?

You will either have to introduce additional binary variables definining if
B[i,j] is zero, or accept inaccuracies, e.g. in:

-M * sum{i in I, j in J} B[i,j] <= A[i] <= M * sum{i in I, j in J} B[i,j];

Best regards

Xypron

-------- Original-Nachricht --------
> Datum: Wed, 3 Oct 2012 09:55:18 -0700 (PDT)
> Betreff: [Help-glpk] Specifying a constraint in CPLEX notation

> I'm doing basis pursuit using glpsol w/ input in CPLEX LP format. This has
> worked extremely well, but I decided to modify my problem formulation and
> have gotten myself into trouble.
>
> The new problem formulation is:
>
> D[k] = sum(i in m)(A[i] + sum(j in n)( B[i][j]*S[j][k]))
>
> where the A[i] & B[i][j] are unknowns.
>
> I want to constrain A[i] to be zero if all the B[i][j] in n are zero.
>
> A[i] is free
> B[i][j] >= 0
>
> m < 10
> n < 300
>
> Can I do this in CPLEX LP format or do I need to switch to another
> notation or C?   Are there any references on doing this?
>
> The closest thing I found was section 20.2 in the AMPL book, but I don't
> see how to apply that to my problem. I'm a geoscientist and a long way from
> home.  So even the obvious can be baffling to me.
>
> Thanks,
> Reg
>
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