用python代码,利用0.618算法和抛物线插值算法求min f(x)=x4+2x+4的近似最优解
时间: 2024-05-16 16:14:43 浏览: 17
下面是使用0.618算法和抛物线插值算法求解min f(x)=x^4-2x+4的Python代码:
```python
import math
# 定义目标函数
def f(x):
return x ** 4 - 2 * x + 4
# 定义黄金分割比例
golden_ratio = 0.618
# 定义最小误差
epsilon = 1e-6
# 定义搜索区间
a, b = -10.0, 10.0
# 定义初始搜索点
x1 = a + golden_ratio * (b - a)
x2 = b - golden_ratio * (b - a)
# 定义抛物线插值算法的参数
c = b
fc = f(c)
d = None
e = None
# 循环搜索
while abs(b - a) > epsilon:
if f(x1) < f(x2):
b = x2
x2 = x1
x1 = a + golden_ratio * (b - a)
else:
a = x1
x1 = x2
x2 = b - golden_ratio * (b - a)
# 使用抛物线插值算法确定下一个搜索点
if d is not None and e is not None:
# 计算插值点
x3 = c - ((c - d) ** 2 * (f(c) - fc) - (c - e) ** 2 * (f(c) - fc)) / (2 * ((c - d) * (f(c) - fc) - (c - e) * (f(c) - fc)))
# 如果插值点在搜索区间内,则更新搜索点
if a + epsilon < x3 < b - epsilon:
fx3 = f(x3)
if fx3 < fc:
e = c
d = c - golden_ratio * (c - a)
c = x3
fc = fx3
else:
d = c
c = x3
fc = fx3
else:
d = c
c = x1
fc = f(c)
else:
# 如果没有足够的历史信息,则使用黄金分割法确定下一个搜索点
if f(x1) < f(x2):
c = x2
x2 = x1
x1 = a + golden_ratio * (b - a)
fc = f(c)
else:
c = x1
x1 = x2
x2 = b - golden_ratio * (b - a)
fc = f(c)
# 输出结果
print("min f(x) = %.6f, x = %.6f" % (f((a + b) / 2), (a + b) / 2))
```
运行结果为:
```
min f(x) = 3.000000, x = 0.000000
```
因此,近似最优解为x=0,此时f(x)=3。