
From:  Yaron Kretchmer 
Subject:  Re: [Helpglpk] complex constraints in glpk 
Date:  Wed, 22 Aug 2007 00:04:57 0700 
> Is it possible to capture constraints of the form
> max(a,b)  min(c,d) > X or max(e,f)  min(g,h) > Y
>
> in glpk?
Nonlinear constraints are not allowed in glpk. However, you can
reformulate them using binary variables.
Let f(t) = (if t < 0 then 0 else t). Then, obviously,
max(p,q) = p + f(q  p)
min(p,q) = p  f(p  q)
Assuming that t_min <= t <= t_max the function f(t) can be modeled as
follows:
t = t1 + t2
f = t2
(1  z) * t_min <= t1 <= 0
0 <= t2 <= z * t_max
where z is a binary variable (z = 0 means that t_min <= t <= 0 and
z = 1 means that 0 <= t <= t_max).
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