SciPy constraints do not work properly when I try to minimize the objective function-CodePudding

I have the following simple python code:

from scipy.optimize import minimize

def cons_function(x):

    return x[0] - 1000

def objective(x):
    a = x[0]
    
    return a ** 5

x0 = [0]
cons_dict = [{'type':'ineq', 'fun': cons_function}]
res = minimize(objective, x0, constraints=cons_dict)

print('x: ', res.x)
print('fun: ',res.fun)

And the output is as follows:

x:  [-2.64828354e 12]
fun:  -1.3026339977067573e 62

But the value of x is supposed to be greater than 1000. And the minimum value of the objective function would be 10e 15.

CodePudding user response：

please check the documentation for the methods that you are using. Depending on the methods of optimization, constraints are used or even ignored. https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.minimize.html

Note

If not given, chosen to be one of BFGS, L-BFGS-B, SLSQP, depending on whether or not the problem has constraints or bounds.

CodePudding user response：

Your initial guess x0 is not feasible and contradicts your constraint as you can see by checking the return optimization result res:

     fun: -1.3026339977067573e 62
     jac: array([2.45939306e 50])
 message: 'Inequality constraints incompatible'
    nfev: 50
     nit: 16
    njev: 15
  status: 4
 success: False
       x: array([-2.64828354e 12])

You always have to use a feasible initial guess that satisfies all your constraints. Note also that your constraint is a simple bound on the variable, so it's recommended to pass it as a bound instead of the more general constraints:

from scipy.optimize import minimize

def objective(x):
    a = x[0]
    return a ** 5

# 1000 <= x[0] <= None is equivalent to 1000 <= x[0] <= Inf
bounds = [(1000, None)]
x0 = [1002]
res = minimize(objective, x0, bounds=bounds)

print('x: ', res.x)
print('fun: ',res.fun)