Welcome to Function Optimisation

This app implements the gradient descent optimisation algorithm to minimise a function

Optimize function f(x)=x2+3x+2

This AI web app implements the gradient descent optimization algorithm to minimize the function f(x)=x2+3x+2. Below is a detailed explanation of each step and the concepts used:

1. The learning rate

The learning rate is a crucial parameter in the gradient descent algorithm, determining the size of the steps taken towards the minimum.

2. Initialization

The function optimizeFunction() initializes several variables:

3. Gradient Descent Loop

The core of the algorithm is a loop that repeatedly updates x to move towards the minimum of the function. Key components include:

4. Convergence Check

After each update, the algorithm checks whether the absolute difference between the current and previous x values is less than the tolerance. This condition checks for convergence, i.e., whether further iterations are unlikely to produce significant changes, indicating that the minimum (or a local minimum) is reached.

5. Output

Once the loop exits, the final values of x and f(x) are displayed. This gives the optimal x that minimizes the function along with the corresponding function value.

6. Additional Function

The calculateFunctionValue(x) function is a helper that computes f(x) for any x. It's used to show the optimized function value at the end of the process.

AI Terminology:

Function

Function f(x)=x2+3x+2