Python cvxpy - reuse some constraints - python-3.x

Question

I'm currently using cvxpy to optimize a really big problem but now facing the current issue.
I run multiple iterations of the solver (every iteration reduces the flexibility of some variables).
Every run has 50 constraints in total, of which only 2 of them are different on every run. The remaining 48 constraints are identical.
During every iteration I rebuild from scratch those 2 constraints, the problem, and the obj function.
If I don't rebuild the remaining (same) 48 constraints, the final solution makes no sense.
I read this post CVXPY: how to efficiently solve a series of similar problems but here in my case, I don't need to change parameters and re-optimize.
I just managed to prepare an example that shows this issue:
x = cvx.Variable(3)
y = cvx.Variable(3)
tc = np.array([1.0, 1.0,1.0])
constraints2 = [x >= 2]
constraints3 = [x <= 4]
constraints4 = [y >= 0]
for i in range(2):
if i == 0:
constraints1 = [x - y >= 0]
else:
x = cvx.Variable(3)
y = cvx.Variable(3)
constraints1 = [x + y == 1,
x - y >= 1,
x - y >= 0,
x >= 0]
constraints = constraints1 + constraints2 + constraints3 + constraints4
# Form objective.
obj = cvx.Minimize( (tc.T # x ) - (tc.T # y ) )
# Form and solve problem.
prob = cvx.Problem(obj, constraints)
prob.solve()
solution_value = prob.value
solution = str(prob.status).lower()
print("\n\n** SOLUTION: {} Value: {} ".format(solution, solution_value))
print("* optimal (x + y == 1) dual variable", constraints[0].dual_value)
print("optimal (x - y >= 1) dual variable", constraints[1].dual_value)
print("x - y value:", (x - y).value)
print("x = {}".format(x.value))
print("y = {}".format(y.value))
As you can see, constraints2 requires all the values in the x vector to be greater than 2. constraints2 is added in both iterations to "constraints" that is used in the solver.
The second solution should give you values of vector x that are less than 2.
Why? How to avoid this issue?
Thank you

Answer 1

You need to use parameters as described in the linked post. Suppose you have the constraint rhs >= lhs which is sometimes used and other times not, where rhs and lhs have dimensions m x n. Write the following code:
param = cp.Parameter((m, n))
slack = cp.Variable((m, n))
param_constraint = [rhs >= lhs + cp.multiply(param, slack)]
Now to turn off the constraint, set param.values = np.ones((m, n)). To turn the constraint on, set param.values = np.zeros((m, n)). You can turn some entries of the constraint off/on by setting some entries of param to be 1 and others to be 0.