Python to solve the optimization problem-use the golden section method to solve the extreme point of the unimodal function

Python to solve the optimization problem-use the golden section method to solve the extreme point of the unimodal function

Algorithm principle

Algorithm Description

Algorithm implementation

def func(x):  # 目标函数
    return x**2 + x + 5


a = -100  # 初始左区间
b = 100  # 初始右区间
p = a + 0.382 * (b - a)  # 计算p
funcp = func(p)  # 计算f(p)
q = a + 0.618 * (b - a)  # 计算q
funcq = func(q)  # 计算f(q)
while (1):
    if (funcp <= funcq):  # f(p)<=f(q), 说明极小值点在(a,q)
        if (q - a <= 0.00001):  # 当区间足够小时, 则终止, 这里q一定大于a;
            print(p)  # 输出极小值点, 输出p或a, 甚至(p,a)中的任一值都可以;
            break
        else:
            b = q  # 下一个右区间b=q;
            q = p  # 根据黄金分割法的定义, 下一次计算的q等于上次的p
            funcq = funcp  # 同样, 下次计算的f(q)等于上次的f(p)
            p = a + 0.382 * (b - a)  # p要重新计算
            funcp = func(p)  # f(p)也要重新计算
    else:
        if (b - p <= 0.00001):  # 以下同理
            print(q)
            break
        else:
            a = p
            p = q
            funcp = funcq
            q = a + 0.618 * (b - a)
            funcq = func(q)