BIGM Relaxation for a linear disjunction

Suppose the following disjunction with i terms:

The "Big-M" relaxation for the previous disjunction can be defined as follows:

Where Mi is a parameter whose value is large enough such that if yi = 0, then (2) becomes redundant. If yi = 1 then constraint aiTx <= bi must be satisfied. The tightest value for Mi is given by:

As an illustration, consider the following disjunction:


The feasible region for the disjunction is:

The Big-M relaxation of (5) is given by:

The feasible region of the BigM relaxation is: