Numerical Optimization using Grid Search and Newton-Raphson

This repository contains an implementation of two numerical optimization methods — Grid Search and Newton-Raphson — for finding the maximum of a given mathematical function.

Project Overview

Assignment Description

The project compares the performance of Grid Search and Newton-Raphson methods in optimizing a mathematical function f: R^2 -> R. Both methods compute the maximum value of the function within specific constraints and measure the number of function calls made during execution.

Key Functions

1. gridsearch: Uses a brute-force grid search algorithm to find the maximum of the function ( f ) over a defined interval with a given precision.
2. newton: Implements the Newton-Raphson method to find the maximum of the function ( f ) using its gradient and Hessian matrix.

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Getting Started

Prerequisites

This project requires Python 3.x. No additional libraries are needed.

Files

• optimization_project.py: Python script containing the implementations of gridsearch and newton functions.
• Documentation: This README and the assignment description document provide details about the methods and implementation.

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Usage

Running the Code

1. Clone this repository.

2. Open optimization_project.py in your favorite Python IDE or text editor.

3. The code includes predefined test cases:

   • Newton-Raphson:

     newton([0,0], 0.001, f, f1, f2)

     Tests the method with an initial guess of ([0, 0]) and ( epsilon = 0.001 ).
   • Grid Search:

     gridsearch([-10,-10], [10,10], 0.01, f)

     Tests the method over the interval ([-10, 10]) for both dimensions with a precision of ( 0.01 ).

4. Run the script:

   python optimization.py