即使Scipy.optimize.minimize看到最小值，它也不会给出最小值 [英] Scipy.optimize.minimize is not giving the minimum value even though it sees that value

问题描述

我正在使用scipy.optimize.minimize为我的目标函数找到最佳参数.

I am using scipy.optimize.minimize to find optimal parameters for my objective function.

我的代码:

import numpy as np
from scipy.optimize import minimize
from scipy.optimize import Bounds

bounds = Bounds([26,26,8,6,400,100,0,25,2],[36,38,28,28,1800,800,100,50,7])

energy_history = []
x_values = []

def objective(x):
    x_trail = x.reshape(1,-1)
    x_trail = sc_X.transform(x_trail)
    y_trail = regressorSVR.predict(x_trail)
    y_trail = y_trail.reshape(1,-1)
    y_trail = sc_Y.inverse_transform(y_trail)
    return y_trail[0]


def callback(x,y):
    fobj = objective(x)
    energy_history.append(fobj)
    x_values.append(x)

x0 = np.array([26,28,15,7,400,377,40,43,4.3])
res = minimize(objective, x0, method='trust-constr',
               options={'verbose': 1}, bounds=bounds,callback=callback)

optimal_values = res.x
energy = res.fun

在给定初始值的情况下，我得到的最小值(res.fun)为-7.1.我正在创建一个列表(energy_history)，以查看它如何达到此值.我在该列表中看到了一些小于-7.1的值，但是为什么-7.1被作为最小值返回.

With the initial values given, the minimized value(res.fun) that I get is -7.1. I am creating a list(energy_history) to see how it is reaching this value. I see some values which are less than -7.1 in that list, but still, why is -7.1 being returned as the minimal value.

在很多时候目标函数达到-21的值，但是为什么仍然返回-7的最小值?

There are multiple times where objective function reached a value of -21, but why is still -7 being returned as a minimum ?

推荐答案

如果我们看一下

If we take a look at the scipy.optimization documentation we can see that scipy.optimize.minimize is listed under local optimization. The main problem is that your problem is non-convex and thus scipy.optimize.minimize cannot guarantee the proper convergence. As it's also very much non-differentiable, many algorithms won't be suited at all.

scipy.optimize确实提供了一些全局优化算法，尽管可以在文档页面上的全局优化下找到它们，即basinhopping，brute和differential_evolution.请查看此答案以获取一些简短说明.

scipy.optimize does provide some global optimization algorithms though that can be found on the documentation page under global optimization, namely basinhopping, brute, and differential_evolution. Look at this answer for some short explanation.

基本上，您可以先尝试brute，仅查看任何系统性问题.从根本上讲，这是一种蛮力解决方案，并且会很慢，但要找到最低要求.更复杂的方法是使用differential_evolution.由于您的功能并不是很流畅，因此basinhopping可能无法正常工作，但是仍然值得一试，并且收敛速度最快.

Basically you can try brute first, just to see any systematic problems. It's basically a brute force solution and will be slow, but find your minimum. The more sophisticated method would be using differential_evolution. Since your function isn't really smooth, basinhopping might not work, but it's still worth a shot and would probably converge the fastest.

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