黄金分割法（Golden Section Method）和斐波那契法（Fibonacci Method）极为相似，唯一的区别就是试探点的公式不一样而已。相比较，斐波那契法更为灵活更为强大。斐波那契法介于二分搜索和黄金分割法之间。
Fibonacci数列：1，1，2，3，5，8，13，21，34，55，89，144......
可见，相邻两项的比值从0.5渐渐变为0.618并趋近于0.618。
黄金分割法的算法如下：
斐波那契法算法如下：
Python程序：
所用函数如下：
f(x)=min{x/2, 2-(x-3)^2, 2-x/2}
# -*- coding: utf-8 -*-
# @Author : ZhaoKe
# @Time : 2022-10-09 15:29
import numpy as np
def fun(x):
f1 = x / 2
f2 = 2-(x-3)**2
f3 = 2-x/2
f = np.vstack((f1, f2, f3))
# print(f)
return -np.min(f, axis=0)
def golden_section(f, left, right, eps):
print("===========Golden Section Search==========")
lam = left + 0.382*(right-left)
mu = left + 0.618*(right-left)
k = 1
tol = right - left
flam, fmu = 0, 0
while tol > eps and k < 100000:
flam = f(lam)
fmu = f(mu)
if flam > fmu:
left = lam
lam = mu
mu = left + 0.618*(right-left)
else:
right = mu
mu = lam
lam = left + 0.382*(right-left)
k = k + 1
tol = np.abs(right-left)
if k == 100000:
print("找不到最小值")
x = None
minf = None
return
x = (left + right) / 2
min_f = f(x)
print("极值点：", x, "，函数值: ", min_f)
def fibonacci_search(f, left, right, eps):
print("===========Fibonacci Search==========")
N = (right-left) / eps
n = 1
Fib = [1, 1]
c = Fib[1] - N
flam, fmu = 0, 0
while c < 0:
n += 1
Fib.append(Fib[n-1] + Fib[n-2])
c = Fib[n] - N
print(Fib[0:12])
lam = left + Fib[n-2]/Fib[n] * (right - left)
mu = left + Fib[n-1]/Fib[n] * (right - left)
k = 1
while k < n-3:
flam = fun(lam)
fmu = fun(mu)
if flam > fmu:
left = lam
lam = mu
mu = left + Fib[n-1-k]/Fib[n-k] * (right-left)
else:
right = mu
mu = lam
lam = left + Fib[n-2-k]/Fib[n-k] * (right-left)
k += 1
x = (left + right) / 2
min_f = f(x)
print("极值点：", x, "，函数值: ", min_f)
if __name__ == '__main__':
golden_section(fun, 0, 8, 0.05)
fibonacci_search(fun, 0, 8, 0.03)
计算结果：
===========Golden Section Search==========
极值点： 2.013992448832476 ，函数值: [-0.99300378]
===========Fibonacci Search==========
[1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144]
极值点： 2.0053050397877983 ，函数值: [-0.99734748]
显然两个算法所得结果都与真实值极为相近（见上图。）
标签：Fib,right,契法,lam,......,斐波,mu,print,left From： https://www.cnblogs.com/zhaoke271828/p/16772439.html