Fletcher-Reeves Optimization Visualizer

This repository contains a MATLAB implementation of the Fletcher-Reeves Conjugate Gradient Method for optimizing a quadratic function. The script visualizes the optimization process using a contour plot, showing the path to convergence at the function's minimum point.

This code was developed as part of our Optimization course project at IASBS, in collaboration with my groupmate, Erfan Faridi.

Features

• Contour Plot Visualization: Displays the function's contour plot and tracks the optimization steps.
• Fletcher-Reeves Update: Implements the Fletcher-Reeves formula for updating the conjugate gradient direction.
• Dynamic Learning Rate: Recalculates the learning rate at each iteration to ensure optimal convergence.
• Convergence Check: Iterates until the solution meets a specified tolerance.
• Detailed Results: Outputs the number of iterations, the minimum point, and the function value at convergence.

Prerequisites

• MATLAB R2016b or later.
• Symbolic Math Toolbox.

Getting Started

Clone the Repository

git clone https://github.com/username/Fletcher-Reeves-Optimization-Visualizer.git
cd Fletcher-Reeves-Optimization-Visualizer

Run the Script

1. Open fletcher_reeves_visualizer.m in MATLAB.
2. Run the script.

Output

• The script will display:
  • The number of iterations to convergence.
  • The coordinates of the minimum point.
  • The minimum value of the function.
• A contour plot with the optimization path overlaid.

Customization

• Initial Point: Modify the initial point x:

  x = [-2; 2.5];

• Tolerance: Adjust the stopping criteria:

  if (errorAmountx1 < 10e-8 && errorAmountx2 < 10e-8)

• Function: Replace the function f with your desired quadratic function:

  f(x1, x2) = (10 * x1 ^ 2) - (4 * x1 * x2) + (x2 ^ 2);

Example Output

The script minimizes the function:

[ f(x_1, x_2) = 10x_1^2 - 4x_1x_2 + x_2^2 ]

and outputs the minimum point, function value at the minimum, and visualizes the optimization path.

Acknowledgments

• MATLAB Documentation: Symbolic Math Toolbox
• Fletcher-Reeves Method: Wikipedia