[Scip] Nonlinear problem

[Julio Rojas]

Thanks Stefan. BTW, it should be max_j(x_j p_ij) - min_j(x_j p_ij). A
mistake on my document.

Now, being a complete newbie on reformulation, can you give me some tips?

Regards.
-------------------------------------------------
Julio Rojas
jcredberry at gmail.com



On Wed, Sep 14, 2011 at 4:52 PM, Stefan Vigerske
<stefan at math.hu-berlin.de> wrote:
> Hi,
>
> I assume that the x_i,y_i,x_j,y_j are fixed parameters.
> If you find a linear formulation for the a_i^x, a_i^y (maybe with additional
> binary variables), then the only nonlinearity left is
> A = a_i^x a_i^y, which SCIP can handle.
> You could model this with ZIMPL, for example.
>
> The function min_j(x_j p_ij) - max_j(x_j p_ij) seems piecewise linear and
> concave for me. It a_i^x >= min_j(x_j p_ij) - max_j(x_j p_ij) is sufficient
> (because equality may be assumed in an optimal solution?), then you could
> reformulate this inequality as a set of linear constraints.
>
> Stefan
>
>> Dear all. I have to solve a problem that has a linear objective
>> function, but some nonlinear constraints. Please, see the attached pdf
>> in order to understand the problem. Is it possible to solve it with
>> SCIP? Is there a way to linearize it in case SCIP is not able to solve
>> it directly?
>>
>> Thanks in advance. Best regards.
>> -------------------------------------------------
>> Julio Rojas
>> jcredberry at gmail.com
>>
>>
>>
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>
>
> --
> Stefan Vigerske
> Humboldt University Berlin, Numerical Mathematics
> http://www.math.hu-berlin.de/~stefan
>