Implementation of Key Optimization Theory Algorithms Using MATLAB

In this article, we explore several key algorithms from optimization theory that can be implemented using MATLAB. These algorithms include the Steepest Descent Method, Interior Point Method, Exterior Point Method, and Interpolation Method. The Steepest Descent Method serves as a fundamental optimization algorithm that minimizes function gradients to locate optimal solutions, typically implemented through iterative updates using gradient information and step size calculations. The Interior Point Method is commonly applied to linear programming problems, transforming constrained optimization into a sequence of unconstrained subproblems solved at interior points using barrier functions and Newton's method iterations. The Exterior Point Method operates similarly but solves subproblems at exterior points using penalty functions to handle constraints. The Interpolation Method approximates objective functions using interpolating functions, which can be linear, quadratic, or higher-order polynomials, often implemented through function evaluation at sample points and polynomial fitting techniques. Each algorithm presents distinct advantages and limitations, making algorithm selection crucial for addressing specific optimization problems in practical applications where factors like convergence speed, constraint handling, and computational efficiency must be considered.