Convex generalized disjunctive programming (GDP)

Edited By: Nicholas Schafhauser, Blerand Qeriqi, Ryan Cuppernull

Methodology

The two most common ways of reformulating a GDP problem into an MINLP are through Big-M (BM) and Hull Reformulation (HR). BM is the simpler of the two, while HR results in tighter relaxation (smaller feasible region) and faster solution times. (https://kilthub.cmu.edu/articles/A_hierarchy_of_relaxations_for_nonlinear_convex_generalized_disjunctive_programming/6466535)

Below is an example of the reformulation of the GDP problem from the Theory section reformulated into an MINLP by using the Big-M method.

${\begin{aligned}\min z=f(x)\\s.t.g(x)<=0\\m_{i}\geq 0,\quad \forall i\in I\\y_{j}\in {0,1},\quad \forall j\in J\end{aligned}}$