I was wondering why it is not OK to model binary (integer) variables of an optimization problem, in the following form
x(x-1) = 0
What are the consequences for an NLP (solved with IP)? Isn't it better to avoid converting an NLP problem to an MINLP? What are the other modeling options available (not decomposition)?
In practice that does not work very well. The problem is that this introduces a nasty non-convexity. Also if this would really be a good idea then we would not need MINLP solvers (or even MIP solvers) at all. All the effort to develop those solvers would have been wasted.