How to add quadratic constraint in conditional indicator constraints in grubipy - gurobi

Question

I am trying to add a conditional indicator constraint using addGenConstrIndicator . E.g. a simple example like this:
import gurobipy as gp
m = gp.Model()
x = m.addVar(vtype=GRB.BINARY, name="x")
y = m.addVar(lb=-10, ub=10, name="y")
m.addGenConstrIndicator(x, True, y <= 4)
However, unfortunately in my case the constraint is not linear and it is quadratic but adding quadratic constraints like:
m.addGenConstrIndicator(x, True, y**2 <= 4)
seems to be not acceptable. I want to know is there another way or any sort of hack or workaround to this that I can add my quadratic constraint in the same way?
My real constraint is the following:
i = model.addVars(gurobi_variants, name='i', vtype=GRB.BINARY)
n = model.addVars(gurobi_replicas, name='n', vtype=GRB.INTEGER, lb=1, ub=scaling_cap)
b = model.addVars(gurobi_batches, name='b', vtype=GRB.INTEGER, lb=1, ub=batching_cap)
for stage in stages:
     for variant in stages_variants[stage]:
          model.addConstr((i[stage, variant] == 1) >> ((n[stage] * b[stage] - arrival_rate * func_l(b[stage], latency_parameters[stage][variant])) >= 0), f'throughput-{stage}')
all the other none Gurobi parameters like stage are constants in the above example. The terms:
n[stage] * b[stage]
is making it quadratic.

Answer 1

The function Model.addGenConstrIndicator() requires a linear constraint (a LinExpr object). However, you can accomplish what you need by modeling the logic yourself. Let's use your first example with x and y. What you want is to enforce the constraint y2 ≤ 4 when x = 1, and relax this constraint when x = 0. You can do this by adding a large value to the right side only when x = 0. Specifically:
RHS = 4
bigM = max(y.LB**2, y.UB**2)-RHS # == 96
m.addConstr(y**2 <= RHS + bigM*(1-x))