MATLAB Implementation of Steepest Descent Gradient Method

This document presents a comprehensive overview of the steepest descent gradient method, a classical optimization algorithm in mathematics, along with its corresponding MATLAB implementation. The steepest descent method is primarily used for finding the minimum of convex functions. In this algorithm, each iteration moves in the direction of the negative gradient at the current point, with the step size determined through one-dimensional linear search. The implementation typically involves calculating partial derivatives using MATLAB's gradient functions or numerical differentiation methods, followed by an efficient line search algorithm (like golden section search or Armijo rule) to optimize convergence. This approach yields satisfactory approximate solutions for convex function minimization problems. We will elaborate on the algorithm's fundamental principles and mathematical formulations, while providing a complete MATLAB program that includes error tolerance settings, convergence criteria checks, and visualization tools for tracking optimization progress. This implementation serves as an excellent educational resource for further study and practical application of optimization techniques.