[Help-glpk] function

[Zvonko Bregar]

Hi,

 

My name is Zvonko Bregar.

 

Please help me with the following problem.

 

There is a real variable P having disjunct definition area {0} + [PMIN, PMAX].

There is also a binary variable X helping in this definition.

If X = 0 then P = 0

And if X = 1 then PMIN < P < PMAX.

So variables X an P work simultaneously.

This should be a rather standard construction.

 

The question is to construct another variable, say R, from X an P

Such that

If X = P = 0 then also R = 0

Else R = min {P-PMIN,PMAX-P}

 

In other words, R measures the minimal distance of P to its boundaries PMIN and PMAX.

But if P = 0 then R must be set to 0 too.

 

For example, if PMIN = 200 and PMAX = 400, than the required function should be something like the “upside down” absolute value function:

 

R =  - | P - 300 | + 100  if 200 < P < 400

 

But also R = 0 if P = 0.

 

I have been trying this for quite some time but didn’t succeed. It looks simple and perhaps there is a simple solution? Or perhaps this cannot be done at all?

 

Thank you

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