Re: [AMPL 6528] any hint to linearize max and min

[Piotr Kałamucki]

Hi,

y = min(a,b) is basically :

if (a>b) then y=b else y=a

you can make it linear with a little help of this link:

http://www.yzuda.org/Useful_Links/optimization/if-then-else-01.html

Regards

2013/1/29 hesam eivazy <hesam...@gmail.com>

Hi All

I am trying to linearize x*[min(a, S+d)-max(b,S)] where a, b, an d are parameters, S is continuous variable, x is binary variable.

Thanks   

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[Robert Fourer]

I would suggest thinking of the subexpression

 

   min(a,S+d) - max(b,S)

 

as a single (concave) piecewise-linear function of S, which you can represent using AMPL's piecewise-linear expression notation (chapter 17 in the AMPL book, www.ampl.com/BOOK/download.html).  Then your entire expression is Z where

 

   x = 0 ==> Z = 0 else Z = Y

   Y = <piecewise-linear expression>

 

You can use the ==> ("implies") operator with CPLEX, but in general you can replace it with a couple of linear mixed-integer constraints.

 

Bob Fourer

4...@ampl.com

 

 

From: am...@googlegroups.com [mailto:am...@googlegroups.com]

On Behalf Of hesam eivazy
Sent: Monday, January 28, 2013 6:33 PM
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Subject: [AMPL 6528] any hint to linearize max and min