MATLAB Implementation of Gradient Methods, Interior Point Methods, Exterior Point Methods, Penalty Functions, and Linear Gradient Approach

In this documentation, we explore various optimization algorithms and their implementations in MATLAB. Specifically, we cover gradient methods, interior point methods, and exterior point methods, along with detailed discussions on penalty function approaches for constraint handling in optimization problems. The gradient method implementation includes both standard and linear variants, utilizing MATLAB's matrix operations for efficient computation. Our interior point method code focuses on barrier functions for constrained optimization, while the exterior point method employs penalty functions to handle constraints externally. The penalty function implementations feature both quadratic and exact penalty methods with adaptive parameter tuning. All source codes are provided with clear parameter input prompts and include error handling for robust execution. By following the interactive prompts, you can directly run these algorithms and apply them to your specific optimization challenges. Each method includes comments explaining key computational steps, such as gradient calculations using finite differences or analytical derivatives, step size selection strategies, and convergence criteria checking. This documentation aims to help you better understand and effectively utilize these optimization techniques in practical applications!