BIGM Relaxation for a linear disjunction
Suppose the following disjunction with i terms:
 |
(1) |
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:
Example:
As an illustration, consider the following disjunction:
 |
(5) |
The feasible region for the disjunction is:
The Big-M relaxation of (5) is given by:
 |
(BM1) |
The feasible region of the BigM relaxation is:
