Unconstrained Optimization Problem Source Code Collection

This article provides a compressed package containing source code implementations for several widely-used unconstrained optimization problem solving methods. These algorithms include: Variable Rotation Method (variable_rotation.m) which cyclically optimizes along coordinate directions, Steepest Descent Method (steepest_descent.m) implementing gradient-based optimization with line search, Modified Newton's Method (modified_newton.m) featuring Hessian matrix regularization for improved convergence, and Conjugate Gradient Method (conjugate_gradient.m) utilizing conjugate directions for efficient large-scale optimization. Additionally, the package includes several utility functions: coefficient_matrix.m that generates the coefficient matrix for quadratic objective functions, minval.m that implements minimum value computation through function evaluation and comparison, and gradient.m that calculates numerical or analytical gradients using finite differences or symbolic differentiation. These MATLAB implementations provide comprehensive tools and materials to help researchers and practitioners better understand and solve unconstrained optimization problems, with each algorithm containing proper initialization, iteration controls, and convergence criteria.