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Re: [Help-glpk] min() & max() functions alternatives to use non numeric

From: Suleyman Demirel
Subject: Re: [Help-glpk] min() & max() functions alternatives to use non numeric parameters
Date: Thu, 28 Apr 2011 11:15:34 -0400

Andrew, you suggest that  z= -max(x, y)  (negative of max) can be modeled  through min, not z=max(x,y), is that right?

On Wed, Apr 27, 2011 at 4:46 PM, Andrew Makhorin <address@hidden> wrote:
> I've got a problem with the max() and min() functions...
> i need to do something like this:
> min(120,ScorteIniziali+PrimoStd+PrimoStra)*70
> in my "objective function"
> but min() accepts only numeric parameters..
> is there any alternatives?

A non-linear objective function like this

  maximize z = min(x1, x2) + min(x3, x4) + ...

can be modeled within mip as follows:

  z =  min_x1_x2 + min_x3_x4 + ...

  s.t. min_x1_x2 <= x1
       min_x1_x2 <= x2
       min_x3_x4 <= x3
       min_x3_x4 <= x4
       . . .

Note that max(x, y) = -min(-x, -y) that allows you to model objective
terms -max(x, y) thru min.

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