[최적화 이론] 경사하강법

 

import random
import matplotlib.pyplot as plt

def convex_function(x):
    return 0.5 * x**2  # 예제로 사용할 convex 함수: f(x) = 0.5 * x^2

def convex_function_diff(x):
    return x

def plot_convergence(maxiterations = 50, threshold = 0.1):
    x_values = np.linspace(-50, 50, 1000)
    y_values = convex_function(x_values)

    plt.plot(x_values, y_values, label='object Function f(x) = 0.5 * x^2')
    plt.title('Convergence of a Convex Function')
    plt.xlabel('x')
    plt.ylabel('f(x)')

    # 초기값 설정
    initial_x = random.randint(-50, 50)
    learning_rate = 0.1
    iterations = 50

    new_x = initial_x
    x_values_history = []
    for i in range(maxiterations):
        x_values_history.append(new_x)
        gradient = convex_function_diff(new_x)  # f'(x) = x for this example
        next_x = new_x - learning_rate * gradient

        if (abs(new_x - next_x) < threshold):
            print(f"iteration complete! {i}")
            break
        new_x = next_x
        

    plt.scatter(x_values_history, convex_function(np.array(x_values_history)), c='red', label='Convergence Points')
    plt.legend()
    plt.show()

# 수렴 과정 plotting
plot_convergence(50,0.00001)