Gradient Descent Program

This is a simple C++ program that allows users to perform gradient descent on functions with either 2 or 3 parameters. The user can input the number of parameters, learning rate, and other required values to start the gradient descent computation.

How to Use

1. Compile the Program

To compile the program, run the following command: g++ main.cpp -o gradient_descent

2. Run the Program

After compiling, you can run the program by typing: ./gradient_descent

3. Input Parameters

The program will ask you to enter several values:

• Number of parameters: Enter 2 for a function with two parameters or 3 for a function with three parameters.
• Learning rate: Enter the learning rate for the gradient descent (e.g., 0.01).
• Maximum number of iterations: Enter the maximum number of iterations you want the gradient descent algorithm to run (e.g., 1000).
• Tolerance: Enter the stopping tolerance for the gradient magnitude (e.g., 1e-6).

4. Example Output

Enter the number of parameters (2 or 3): 2 Enter the learning rate (e.g., 0.01): 0.01 Enter the maximum number of iterations: 100 Enter the tolerance for stopping (e.g., 1e-6): 1e-6 Iteration 1: Function value = 1.98 Iteration 2: Function value = 1.9602 ... Converged after 50 iterations. Optimized parameters: 0.01 0.01

5. Customizing the Function

You can replace the provided function definitions in the code with your own functions:

• For 2 parameters, modify the function2Params function.
• For 3 parameters, modify the function3Params function.

6. Notes

• The program uses a simple quadratic function as an example (x^2 + y^2 for 2 parameters, and x^2 + y^2 + z^2 for 3 parameters).
• You can replace these with any other differentiable function to perform gradient descent on your custom functions.
• The initial parameter values are set to 1.0, but you can modify this in the code.

Enjoy experimenting with different functions and parameters!