Why scipy.optimize.minimize does not work with a constraint and initial value 0

Question

I am trying to optimize a function of two variables. I want one variable to be fixed at 50 and another be between -5 and 5. I wrote the following code:

x0 = np.array([50, 0.0])
res = minimize(error, x0, constraints=[
    {'type': "eq", "fun": lambda x: x[0] - 50},
    {'type': "ineq", "fun": lambda x: -abs(x[1]) + 5},
])

where minimize is a function from scipy.optimize . The first constraint is x[0] == 50 and second one is -5 <= x[1] <= 5 . I get the following response: message: 'Inequality constraints incompatible' . But when I set the second variable to be not zero (eg x0 = np.array([50, 0.1]) ) it finds a solution successfully. What can be the reason of such behavior?

Answer 1

The constraints need to be differentiable, and your second constraint is not. If you express the constraint in terms of x[1]**2 instead of abs(x[1]) , it should work. You could also eliminate the abs by splitting the constraint into two separate constraints, one for the upper bound and one for the lower bound.