Suppose I wish to express the constraint (X = 0 OR X >= 0.3 Y). We could use logical constraints or use the big M method:

X >= 0.3 Y b
X <= M b

where b is a binary variable. Is there any reason to expect large performance differences between these approaches? Or are they similar enough under the hood?

Another example of the two methods is implementing cardinality, e.g. the two approaches outlined here: binary variable depending on a continuous variable (mixed integer programming in cplex) 

Thanks,
Michael

------------------------------
Michael Han
------------------------------
#DecisionOptimization

Hi,

a good tech note : https://www.ibm.com/support/pages/difference-between-using-indicator-constraints-and-big-m-formulation

regards

------------------------------
[Alex] [Fleischer]
[Data and AI Technical Sales]
[IBM]
------------------------------

Original Message:
Sent: Wed November 30, 2022 05:53 PM
From: Michael Han
Subject: Logical constraints vs explicit formulations

Suppose I wish to express the constraint (X = 0 OR X >= 0.3 Y). We could use logical constraints or use the big M method:

X >= 0.3 Y b

where b is a binary variable. Is there any reason to expect large performance differences between these approaches? Or are they similar enough under the hood?

Another example of the two methods is implementing cardinality, e.g. the two approaches outlined here: binary variable depending on a continuous variable (mixed integer programming in cplex) 

Thanks,
Michael

------------------------------
Michael Han
------------------------------

#DecisionOptimization

That's very helpful, thanks Alex.

------------------------------
Michael Han
------------------------------

Original Message:
Sent: Thu December 01, 2022 04:10 AM
From: ALEX FLEISCHER
Subject: Logical constraints vs explicit formulations

Hi,

a good tech note : https://www.ibm.com/support/pages/difference-between-using-indicator-constraints-and-big-m-formulation

regards

------------------------------
[Alex] [Fleischer]
[Data and AI Technical Sales]
[IBM]

Original Message:
Sent: Wed November 30, 2022 05:53 PM
From: Michael Han
Subject: Logical constraints vs explicit formulations

Suppose I wish to express the constraint (X = 0 OR X >= 0.3 Y). We could use logical constraints or use the big M method:

X >= 0.3 Y b

where b is a binary variable. Is there any reason to expect large performance differences between these approaches? Or are they similar enough under the hood?

Another example of the two methods is implementing cardinality, e.g. the two approaches outlined here: binary variable depending on a continuous variable (mixed integer programming in cplex) 

Thanks,
Michael

------------------------------
Michael Han
------------------------------

#DecisionOptimization