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Re: [Help-glpk] 'not' or 'or' constraints?

From: Stefan Balev
Subject: Re: [Help-glpk] 'not' or 'or' constraints?
Date: Fri, 27 May 2005 11:03:05 +0200
User-agent: Mozilla/5.0 (X11; U; Linux i686; en-US; rv:1.0.1) Gecko/20020830

Philip Warner wrote:

This may not be the right forum for this, but I need to solve an LP problem that is subject to constraints like:

   s <= 0 OR s >= 100

or, rewritten,

   Not (0 < s < 100)

Is this something I can do in GLPK?


By definition this is NOT LP problem and cannot be handled by LP techniques. The main reason is that the feasible set is not convex.

A standard remedy consists in introducing a binary variable x in {0,1} together with the constraints

s <= M x
s >= 100 + M (x - 1)

where M is "sufficiently large". This is a MIP problem and can be handled by glpk.


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