pythonoptimizationcvxpyconvex-optimization

Use or operator in constraint cvxpy

I am trying to use cvxpy but i don't know how to use or operator.

I have

x = cp.Variable(N, integer=True)

I try

x[i]==0 or x>=m[i].

I got this error

> Cannot evaluate the truth value of a constraint or chain constraints, e.g., 1 >= x >= 0.

Then i try:

for i in range(N):
    constraints += [
        x[i]*(x[i]-m[i])>=0,
    ]

And i got

> Problem does not follow DCP rules.

Can someone help me? Thank you

Solution

  • The constraint

     x=0 or x≥L

    is known as x being a semicontinuous variable. Some solvers and tools have specialized facilities for this. Otherwise, add a binary variable y and use:

     y*L ≤ x ≤ y*U
 x ∈ [0,U]        (U is an upperbound on x)
 y ∈ {0,1}