sci.op-research

hpmilton@gmail.com wrote:
> Hello all,
> I have an IP minimization problem in which there are sum of piecewise
> linear functions and other variables. I want to give an example.
> Let one of the piecewise linear functions be:
> f(x,y) = ( 2x+1 if 3> can imagine it has piecewise linear symmetric concave triangular shape
> in the range (3>
> The reason why I am calling it f(x,y) is that this only works when y
> takes values in some range (a<=y<=b). If y is out of this range, then
> no matter what x is, f(x,y) will be a constant value of 7.
>
> Think now that there are a number of different piecewise functions in
> the model with different values of a and b for y.
>
> If there was no y, I could model it using standard piecewise linear
> function tricks. But my brain stopped working at this point.
>
> Any idea.
>
> Thank you.
>

If the pw-linear functions are convex in a minimization objective and
any function <= limit constraints, and concave in a maximization
objective and any function >= limit constraints, then the "usual tricks"
work. In any other cases (convex when they should be concave or vice
versa, neither convex nor concave, discontinuous at discrete points,
...) you'll need to partition the feasible region, which is typically
done by introducing binary variables and appropriate constraints (and
living with the fact that your nice easy LP just became a less-easy MILP).

/Paul