在python中优化输出有约束的输入

【问题标题】：Optimizing input where output has constraints in python在python中优化输出有约束的输入
【发布时间】：2020-10-02 20:00:41
【问题描述】：

我试图将输入（1 个变量）最小化为输出为概率的非线性函数。

如，如果输入为 5，则输出概率为 40%，输入 10，则概率变为 93%。计算概率的函数是确定性的。

现在我想最小化输入，使得概率大于 80% 。有没有使用 scipy 库在 python 中执行此操作的简单方法？

【问题讨论】：

标签： python optimization scipy minimization nonlinear-functions

【解决方案1】：

以下有帮助吗？

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=}')

【讨论】：