sin-x--optimization

This project visualizes gradient descent optimization applied to the function $f(x) = \sin(x)$. It demonstrates how the gradient descent algorithm iteratively updates the input to approach a local minimum of the sine function by using its derivative.

How it works

• The function used is $f(x) = \sin(x)$.
• The derivative used for gradient updates is $f'(x) = \cos(x)$.
• The input domain spans from $-8\pi$ to $8\pi$ with small steps.
• The algorithm starts at $x = \frac{\pi}{4}$.
• In each iteration, the input value is updated by moving opposite to the gradient direction scaled by a learning rate $\alpha = 0.1$:

$$ x_{\text{new}} = x_{\text{old}} - \alpha \times f'(x_{\text{old}}) $$

• The process is animated with matplotlib to show the current point moving along the sine curve toward a minimum.

Usage

Run the script gradient_descent.py to watch the gradient descent visualization in action.
Make sure you have the required dependencies installed:

pip install numpy matplotlib
python gradient_descent.py