Gradient Descent Implementation

This is a Python implementation of the gradient descent algorithm for optimizing a mathematical function. Gradient descent is an optimization technique commonly used in machine learning and mathematical optimization to find the minimum (or maximum) of a function.

Prerequisites

Before you begin, ensure you have met the following requirements:

• [Python 3.x]
• [NumPy]
• [SymPy]

You can install NumPy and SymPy using pip:

pip install numpy
pip install sympy

Usage

• Clone the repository to your local machine or download the code.

• Run the gradient_descent.py script in your Python environment.

• You will be prompted to enter the following inputs:

  • [Mathematical expression of the function you want to optimize.]
  • [Learning rate: The step size for each iteration.]
  • [Number of iterations: The number of times the gradient descent algorithm will run.]
  • [Starting point for x and y.]

• The program will execute the gradient descent algorithm and provide you with the optimal points and the optimal value of the function.

Example

Here's an example of how to use the code:

Enter an expression: x**2 + y**2
Enter the learning rate: 0.1
Enter number of iterations: 100
Enter starting point of x: 2
Enter starting point of y: 2

Output:

Our learning rate is : 0.1
Our number of iterations is : 100
New points in  1 iteration is  1.60000000000000 1.60000000000000
...
New points in  100 iteration is  0.00000000000000 0.00000000000000
Optimal points are :  0.00000000000000 0.00000000000000 and optimal value of the function is :  0.00000000000000