Optimizing input where output has constraints in python

Question

I trying to minimise an input ( 1 variable ) to a non linear function where the output is a probability.

As in, if the input is 5 the output probability is 40% , 10 input the probability becomes say 93%. The function to compute the probability is deterministic.

Now i want to minimise the input such that the probability is greater than say 80% . Is there a simple way of doing this in python using scipy library ?

Answer 1

Does the following help?

import math
from scipy.optimize import minimize,NonlinearConstraint

def fmin(x):
# this is the function you are minimizing
# in your case this function just returns x
    return x

def fprob(x):
# this is the function defining your probability as a function of x
# this function is maximized at x=3, and its max value is 1
  return math.exp(-(x-3)*(x-3))

# these are your nonlinear constraints
# since you want to find input such that your probability is > 0.8
# the lower limit is 0.8. Since probabilty cannot be >1, upper limit is 1
nlc  = NonlinearConstraint(fprob,0.8,1)

# the zero is your initial guess
res = minimize(fmin,0,method='SLSQP',constraints=nlc)

# this is your answer
print(f'{res.x=}')