How to express “if y=1 then 0<=x<=u, if y=0 then x=0”?

[abcdvvvv]

Hi,

I want to model the following typical GDP logic:

• If y = 1, then 0<=x<=u;
• If y = 0, then x == 0.

How should I write this pattern in DisjunctiveProgramming.jl syntax?
I did not find an example of this in the documentation.

A minimal example of what I want:

using DisjunctiveProgramming
model = GDPModel()
@variable(model, y, Logical)
@variable(model, x >= 0)
u = 10.0

# How to write the following two branches?
# (y = 1) --> 0<=x<=u
# (y = 0) --> x == 0

[pulsipher]

Hi @abcdvvvv,

You just need to define a disjunction:

using DisjunctiveProgramming
model = GDPModel()
@variable(model, y[1:2], Logical)
@variable(model, x >= 0)
u = 10.0

@constraint(model, 0 <= x <= u, Disjunct(y[1]))
@constraint(model, x == 0, Disjunct(y[2]))
disjunction(model, y)

I suggest taking a deeper dive into generalized disjunctive programming to learn about disjunctions.

[abcdvvvv]

Hello pulsipher, I understand.

Thank you for your answer!