Linearisation techniques for MINLPs

Question

I am wondering what kinds of linearisations people do for MINLPs outside my field of expertise.

I work in global optimisation, so by "linearisation" we would typically mean one of the following:

• Exact linearisations, i.e., to reformulate a nonlinear structure to LP or MILP
• Convex/concave LP/MILP relaxations of nonlinear functions, e.g., outer approximations, secants, or piecewise relaxations
• Integer cuts to eliminate nonlinear constraints or reduce the domain

What kinds of linearisations do you do? Does the term mean something different in your field? Can you share some examples/references?

Answer 1

In the context of gas networks my former colleagues used (and still use) adaptive linearization techniques combined with other (sometimes nonlinear) heuristics. There is a whole book about the topic which also won the EURO Excellence in Practice Award 2016 for best book on applications of optimization.

Answer 2

I am not sure if you talk about this $z=\prod\limits_{i=1}^{n}x_i$ or the technique described on pages 3, 4 and 5 in this report piecewise linear function. These are the two main approaches used.