0.618代码如下：

import math

# 定义函数h(t) = t^3 - 2t + 1

def h(t):

    return t**3 - 2*t + 1

# 0.618算法

def golden_section_search(a, b, epsilon): 

    ratio = 0.618 

    while (b - a) > epsilon: 

        x1 = b - ratio * (b - a) 

        x2 = a + ratio * (b - a) 

        h_x1 = h(x1) 

        h_x2 = h(x2) 

        if h_x1 < h_x2: 

            b = x2 

        else: 

            a = x1 

    return a  # 或者返回 b，因为它们的值非常接近

# 在 t 大于等于 0 的范围内进行搜索

t_min_618 = golden_section_search(0, 3, 0.001)

print("0.618算法找到的最小值：", h(t_min_618))

基于Armijo准则的线搜索回退法代码如下：

import numpy as np 

  def h(t): 

    return t**3 - 2*t + 1 

  def h_derivative(t): 

    return 3*t**2 - 2 

  def armijo_line_search(t_current, direction, alpha, beta, c1): 

    t = t_current 

    step_size = 1.0 

    while True: 

        if h(t + direction * step_size) <= h(t) + alpha * step_size * direction * h_derivative(t): 

            return t + direction * step_size 

        else: 

            step_size *= beta 

        if np.abs(step_size) < 1e-6: 

            break 

    return None 

  def gradient_descent(start, end, alpha, beta, c1, epsilon): 

    t = start 

    while True: 

        if t > end: 

            break 

        direction = -h_derivative(t)  # 负梯度方向 

        next_t = armijo_line_search(t, direction, alpha, beta, c1) 

        if next_t is None or np.abs(h_derivative(next_t)) <= epsilon: 

            return next_t 

        t = next_t 

    return None 

  # 参数设置 

alpha = 0.1  # Armijo准则中的参数alpha 

beta = 0.5  # Armijo准则中的参数beta 

c1 = 1e-4  # 自定义参数，用于控制Armijo条件的满足程度 

epsilon = 1e-6  # 梯度范数的终止条件 

  # 搜索区间为[0,3] 

start = 0 

end = 3 

  # 执行梯度下降算法，求得近似最小值点 

t_min = gradient_descent(start, end, alpha, beta, c1, epsilon) 

print("求得的最小值点为:", t_min) 

print("最小值点的函数值为:", h(t_min))