MATLAB Implementation of Optimization Algorithms - Golden Section, Gradient Descent, Conjugate Gradient, and Penalty Function Methods

In my research, I have developed multiple optimization algorithms using MATLAB, which include but are not limited to the Golden Section (0.618) method, Gradient Descent, Conjugate Gradient method, and Penalty Function method. These algorithms feature MATLAB implementations with key functions like fminbnd for bracketing in Golden Section, gradient calculations using diff or symbolic math for Gradient Descent, and iterative direction updates in Conjugate Gradient using Polak-Ribière formulas. The Penalty Function method incorporates constraint handling through quadratic penalty terms with adaptive penalty parameters. These optimization techniques find broad applications in mathematical and engineering fields, playing crucial roles in solving practical problems such as optimizing production process efficiency and reducing operational costs. In practical implementations, these algorithms achieve optimal performance through parameter tuning techniques like line search methods and convergence criteria adjustments, providing users with optimal solutions. My research passion for these algorithms drives me to develop more advanced optimization methods in the future, contributing to societal progress through improved computational optimization capabilities.