Solving Unconstrained Optimization Problems Using MATLAB

In this documentation, we will learn how to solve unconstrained optimization problems using MATLAB. We will examine several distinct solution methodologies, including Steepest Descent Method (implemented with gradient computation and line search algorithms), Newton's Method (utilizing Hessian matrix calculations and iterative updates), Conjugate Gradient Method (featuring automatic direction reset mechanisms), Variable Metric Methods (covering both DFP and BFGS quasi-Newton approaches with rank-two updates), and Nonlinear Least Squares (implemented through Gauss-Newton or Levenberg-Marquardt algorithms). Each method will be analyzed with detailed discussions of their respective advantages and limitations, accompanied by practical MATLAB implementation guidelines. For constrained optimization problems, we will investigate Exterior Penalty Function Methods (with penalty parameter adaptation techniques) and Generalized Multiplier Methods (including augmented Lagrangian implementations). The documentation provides comprehensive code examples demonstrating function formulation, algorithm parameter configuration, and convergence monitoring. At the conclusion, you will find specific problem case studies with performance comparisons and professional recommendations for optimizing your MATLAB code through vectorization, preallocation, and algorithm selection criteria.