Re: [Help-glpk] Linear expressions in the integrands of iteratedexpressions

[Barry Rountree]

On Sunday 22 October 2006 20:54, you wrote:
> Can you replace
> 
>   s.t. blrMax:max{i in I, j in J} x[i,j] = 1;
> 
> with just putting an upper bound "x[i,j] <= 1" where you define the
> variable?

That's a very good suggestion, but it doesn't quite handle 
what I'm trying to do.  I'm trying to code up
exclusivity without having to use "binary", e.g. 

    s.t. foo:sum{i in I} x[i] = 42;
    s.t. bar:max{i in I} x[i] = 42;

should ensure that there is one and only one "42" in x[i],
with everything else being zero (assuming all x[i]>=0, of
course).  

This can certainly be done more elegantly in an ILP than 
an LP, and I don't know if an LP still scales better when 
given these kind of constraints.  So I'll be coding up 
one of each flavor and testing.

> "max" isn't a linear operator.

Here's what I've been doing using the C interface to glpk:

   given variables x>=0, y>=0, and z, z=max(x,y) looks like

   -x + z >= 0
   -y + z >= 0
   (indirectly) minimize z

I thought that "max" would have similar functionality.  If
that's not the case because it isn't a linear operator, then
I'll need back up a bit and try a different approach.

So, is "max" not intended for what I'm trying to do?  Did I
get a little too giddy at the thought of abandoning my large
pieces of graph paper for a high-level language?

Thanks,

Barry


> -Marc