Formulating linear constraints

[vtjeng]

You mention that you can do a better job formulating piecewise constraints here. Could you explain what your approach is? (My big-M approach relies on finding the best possible bounds I can on the input, and then using those bounds in the big-M formulation.

(Filing as an issue here because I thought it would be relevant to future users of this library.)

[joehuchette]

All you need to do is give a vector of the discretization points d along the domain of your x variable, and a vector of the corresponding function values fd at each point; you don't need to compute big-M bounds. Then you can impose that z = f(x) (if your function is univariate) with

z = piecewiselinear(model, x, d, fd)

You can optionally specify the formulation you would like to use; you can see our recent paper and the references for more info on the details of the formulations.

[odow]

Closing as stale and because this discussion seems resolved.

[vtjeng]

I seem to have missed this response and only realized it when @odow closed the issue ...

along the domain of your x variable

just to clarify, @joehuchette, do we need the domain to be finite? e.g. if I have f(x) = max(x, 0) then I also need to know what range of values x could take?

[odow]

The d in:

z = piecewiselinear(model, x, d, fd)

is a discrete set of points.

PiecewiseLinearOpt.jl doesn't get to see the expression max(x, 0). It just gets to see the set of points (d, fd).

x will end up being restricted to some convex combination of the domain d.