Convex generalized disjunctive programming (GDP)

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Edited By: Nicholas Schafhauser, Blerand Qeriqi, Ryan Cuppernull


[ Insert picture from google doc of GDP branching to Logic Based Methods and Reformulation MI(N)LP ]



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. (

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.

Notice that the boolean term from the original GDP has been converted into a numerical {0,1}. The logic relations have also been converted into linear integer constraints (Hy).


This MINLP reformulation can now be used in well-known solvers (list them here) to calculate a solution.

Numerical Example

The following example was taken from:

Figure 1: Placeholder

GDP numeric example 2.png GDP numeric example 3.png