Re: [Help-glpk] glpk wikibook, modeling tips

[Robbie Morrison]

Hello Andrew

Changes made, please see:

http://en.wikibooks.org/wiki/GLPK/Modeling_tips#Extremum_terms

On another tack, people might be interested in a
(relatively) new site for collaborative maths, which
has notched up at least one success so far:

  http://polymathprojects.org
  http://en.wikipedia.org/wiki/Polymath_project#Polymath_Project
  http://www.guardian.co.uk/science/2011/may/08/welcome-to-wikimaths
  
http://www.thebigquestions.com/2010/04/08/blogging-tic-tac-toe-and-the-future-of-math

cheers, Robbie

------------------------------------------------------------
To:          Robbie Morrison <address@hidden>
Subject:     glpk wikibook, modeling tips
Message-ID: <address@hidden>
From:        Andrew Makhorin <address@hidden>
Date:        Mon, 09 May 2011 20:46:37 +0400
------------------------------------------------------------

> Robbie,
>
> I noticed an inexactness in the topic
>
> http://en.wikibooks.org/wiki/GLPK/Modeling_tips#Non-convex_functions
>
> You write:
>
>         A nonlinear objective function in the form
>         maximize z = min(x1,x2) + min(x3,x4) + ...
>         can be modeled as an MIP ...
>
> However, the trick is that in this case you don't need
> to use binary variables at all, because you maximize a
> concave objective function (this is the same case as if
> you minimized a convex objective function).  It seems
> to me that it would be better to consider minimization
> case, because it is more obvious.
>
> Best,
>
> Andrew Makhorin

------------------------------------------------------------
To:          Robbie Morrison <address@hidden>
Subject:     Re: glpk wikibook, modeling tips
Message-ID: <address@hidden>
From:        Andrew Makhorin <address@hidden>
Date:        Mon, 09 May 2011 20:52:25 +0400
------------------------------------------------------------

>> It seems to me that it would be better to consider
>> minimization case, because it is more obvious.
>
> That is,
>
>    minimize z = max(x1, x2) + max(x3, x4) + ...
>
> The case
>
>    minimize z = max(x1, x2) + max(x3, x4) - min(x5, x6) - ...
>
> can be reduced to the previous one by substituting
>
>    -min(x5, x6) = max(-x5, -x6)
>
> And the case of maximization
>
>    maximize z = min(x1, x2) + min(x3, x4) - max(x5, x6) - ...
>
> can be reduced to minimization by changing the sign of
> the objective.

---
Robbie Morrison
PhD student -- policy-oriented energy system simulation
Technical University of Berlin (TU-Berlin), Germany
University email (redirected) : address@hidden
Webmail (preferred)           : address@hidden
[from Webmail client]