Forbidden range for a variable of a LP

Specific Domains Optimization (Mathematical)
1

I would like to express a linear program having a variable that can only be greater or equal than a constant P or equal to 0. Like :

x≥P or x=0

I know I could express it as a mixed integer problem but I really need to stay in a pure LP.
Anyone know a kind of trick to workaround it on JuMP?

2

Unfortunately no. It is not LP representable.

3

ok, thanks. Do you know if there’s the same limitation for a constraint like that:

if x1 == 0 
then x2==0

where x1 and x2 are variables of a LP problem ?
Thanks.

4

The only way to achieve something like that is as follows:

model = Model()
@variable(model, x1 >= 0)
@variable(model, x2 >= 0)
@constraint(model, x2 <= x1)

In general, if <condition> type constraints are not LP representable. You may want to consult a linear programming textbook, e.g., Textbook: Introduction to Linear Optimization.

1 Like
5

I see. The only problem is that I can maybe have a x1>=x2 according to the project. So,I ended up with the same limitation of the LP problem :confused:

6

Do you know how I could express it by using the workaround with binary variables and a large number M? I have tried to think but I don’t have a good math background…x1 and x2 are not binary.

7

Yes, but this question is not related to Julia or JuMP.
The OR StackExchange will have an answer to these kinds of modeling questions.