[Scip] Nonlinear problem

[Stefan Vigerske]

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